<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt src="https://files.passeidireto.com/e228eb14-7ade-4ad5-bff0-d10d2cb7b2eb/bg1.png" alt="Pré-visualização de imagem de arquivo"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls7 ws6c">Formulário <span class="blank _0"> </span>para 2ª Ava<span class="blank _0"> </span>liação de Cálculo<span class="blank _0"> </span> Numérico </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls7 ws6c">Interpolação<span class="blank _0"> </span> Polinomial </div><div class="t m1 x3 h3 y3 ff1 fs1 fc0 sc0 ls7 ws6c">Fórmula de Lagrange </div><div class="t m2 x4 h4 y4 ff2 fs2 fc0 sc0 ls7 ws0">0 1<span class="blank _1"> </span>1<span class="blank _2"> </span>1</div><div class="t m2 x5 h4 y5 ff2 fs2 fc0 sc0 ls7 ws1">0 1<span class="blank _3"> </span>1<span class="blank _4"> </span>1</div><div class="c x6 y6 w2 h5"><div class="t m3 x7 h6 y7 ff2 fs3 fc0 sc0 ls7 ws2">(<span class="blank _5"> </span>)( )...(<span class="blank _6"> </span>)(<span class="blank _6"> </span>)...(<span class="blank _5"> </span>)</div></div><div class="t m3 x8 h6 y8 ff2 fs3 fc0 sc0 ls7 ws3">( )</div><div class="c x9 y9 w3 h5"><div class="t m3 x7 h6 ya ff2 fs3 fc0 sc0 ls7 ws4">(<span class="blank _7"> </span>)( )...(<span class="blank _2"> </span>)(<span class="blank _8"> </span>)...(<span class="blank _7"> </span>)</div></div><div class="t m2 xa h7 y4 ff3 fs2 fc0 sc0 ls7 ws5">k k<span class="blank _9"> </span>n</div><div class="t m2 xb h7 yb ff3 fs2 fc0 sc0 ls7">k</div><div class="c xc yc w4 h8"><div class="t m2 x7 h7 yd ff3 fs2 fc0 sc0 ls7 ws6">k<span class="blank _a"> </span>k<span class="blank _b"> </span>k k<span class="blank _c"> </span>k k<span class="blank _d"> </span>k n</div></div><div class="t m3 xd h9 ye ff3 fs3 fc0 sc0 ls7 ws7">x x<span class="blank _e"> </span>x x<span class="blank _f"> </span>x x<span class="blank _10"> </span>x x<span class="blank _11"> </span>x x</div><div class="t m3 xe h9 y8 ff3 fs3 fc0 sc0 ls7 ws8">l x</div><div class="c xf y9 w5 h5"><div class="t m3 x7 h9 ya ff3 fs3 fc0 sc0 ls7 ws9">x x<span class="blank _e"> </span>x x<span class="blank _f"> </span>x x<span class="blank _10"> </span>x x<span class="blank _12"> </span>x x</div></div><div class="t m2 x10 ha y4 ff4 fs2 fc0 sc0 ls7 wsa">− +</div><div class="t m2 x11 ha y5 ff4 fs2 fc0 sc0 ls7 wsb">− +</div><div class="c x12 yf w6 hb"><div class="t m3 x7 hc y10 ff4 fs3 fc0 sc0 ls7 wsc">− −<span class="blank _13"> </span>−<span class="blank _14"> </span>−<span class="blank _b"> </span>−</div></div><div class="t m3 x13 hc y8 ff4 fs3 fc0 sc0 ls0">=<span class="ls7 wsd v1">− −<span class="blank _15"> </span>−<span class="blank _16"> </span>−<span class="blank _17"> </span>−</span></div><div class="t m1 x14 hd y8 ff2 fs1 fc0 sc0 ls7 ws6c">. </div><div class="t m1 x15 hd y11 ff2 fs1 fc0 sc0 ls7 ws6c">Assim para valores dados: <span class="ff3">f</span></div><div class="t m4 x16 he y12 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x17 hf y11 ff3 fs1 fc0 sc0 ls7 wse">=f(x</div><div class="t m4 x18 he y12 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x19 hf y11 ff3 fs1 fc0 sc0 ls7 ws6c">), f</div><div class="t m4 x1a he y12 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x1b hf y11 ff3 fs1 fc0 sc0 ls7 wsf">=f(x</div><div class="t m4 x1c he y12 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x1d hf y11 ff3 fs1 fc0 sc0 ls7 ws6c">), ..., f</div><div class="t m4 x1e he y12 ff3 fs4 fc0 sc0 ls7">n</div><div class="t m1 x1f hf y11 ff3 fs1 fc0 sc0 ls7 wsf">=f(x</div><div class="t m4 x20 he y12 ff3 fs4 fc0 sc0 ls7">n</div><div class="t m1 x21 hd y11 ff3 fs1 fc0 sc0 ls7 wse">)<span class="ff2 ws6c"> de uma função </span><span class="wsf">y=f(x)<span class="ff2 ws6c">, o polinômio: </span></span></div><div class="t m2 x1 h4 y13 ff2 fs2 fc0 sc0 ls7">0</div><div class="c x22 y14 w7 h5"><div class="t m1 x7 hd y15 ff2 fs1 fc0 sc0 ls7 ws10">( )<span class="blank _b"> </span>(<span class="blank _18"> </span>)</div></div><div class="t m2 x23 h7 y16 ff3 fs2 fc0 sc0 ls7">n</div><div class="t m2 x24 h7 y17 ff3 fs2 fc0 sc0 ls7 ws11">n<span class="blank _9"> </span>k k</div><div class="t m2 xb h7 y13 ff3 fs2 fc0 sc0 ls7">k</div><div class="c x25 y14 w8 h5"><div class="t m1 x7 hf y15 ff3 fs1 fc0 sc0 ls7 ws12">P<span class="blank _19"> </span>x<span class="blank _1a"> </span>f l<span class="blank _1b"> </span>x</div></div><div class="t m2 x23 ha y13 ff4 fs2 fc0 sc0 ls7">=</div><div class="t m3 x26 h10 y18 ff4 fs3 fc0 sc0 ls1">=<span class="fs5 ls7 v2">∑</span></div><div class="t m1 xd hd y19 ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y1a ff1 fs1 fc0 sc0 ls7 ws6c">Erro na interpolação </div><div class="t m5 x27 h11 y1b ff2 fs6 fc0 sc0 ls7 ws13">0 1<span class="blank _1c"> </span><span class="ws14 v0">( 1)</span></div><div class="t m6 x2 h12 y1c ff2 fs7 fc0 sc0 ls7 ws15">(<span class="blank _5"> </span>)(<span class="blank _1d"> </span>) ... (<span class="blank _1e"> </span>)</div><div class="c x28 y1d w9 h5"><div class="t m6 x7 h12 y1e ff2 fs7 fc0 sc0 ls7 ws16">(<span class="blank _1f"> </span>)<span class="blank _20"> </span>ma<span class="blank _21"></span>x<span class="blank _22"> </span>( )</div></div><div class="t m6 x29 h12 y1f ff2 fs7 fc0 sc0 ls7 ws17">(<span class="blank _23"> </span>1<span class="blank _24"></span>) !</div><div class="t m5 x2a h13 y1b ff3 fs6 fc0 sc0 ls2">n<span class="ls7 v0">n</span></div><div class="t m5 x5 h13 y20 ff3 fs6 fc0 sc0 ls3">n<span class="ls7 ws18 v3">a t b</span></div><div class="t m6 x2b h14 y1c ff3 fs7 fc0 sc0 ls7 ws19">x x<span class="blank _e"> </span>x x<span class="blank _c"> </span>x x</div><div class="c x12 y1d wa h5"><div class="t m6 x7 h14 y1e ff3 fs7 fc0 sc0 ls7 ws1a">R x<span class="blank _25"> </span>f<span class="blank _26"> </span>t</div></div><div class="t m6 x2c h14 y1f ff3 fs7 fc0 sc0 ls7">n</div><div class="t m7 x2d h15 y1a ff4 fs8 fc0 sc0 ls7">ε</div><div class="t m5 x2e h16 y21 ff4 fs6 fc0 sc0 ls7">+</div><div class="t m5 x2f h16 y22 ff4 fs6 fc0 sc0 ls7 ws1b">≤ ≤</div><div class="t m6 x30 h17 y1c ff4 fs7 fc0 sc0 ls7 ws1c">− −<span class="blank _27"> </span>−</div><div class="t m6 x31 h17 y1a ff4 fs7 fc0 sc0 ls7 ws1d">= ≤<span class="blank _28"> </span>×</div><div class="t m6 x10 h17 y1f ff4 fs7 fc0 sc0 ls7">+</div><div class="t m1 x32 hd y1a ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y23 ff1 fs1 fc0 sc0 ls7 ws6c">Forma de Newton para o polin<span class="blank _0"> </span>ômio interpolador<span class="ff2"> </span></div><div class="t m8 x1 h18 y24 ff2 fs9 fc0 sc0 ls7 ws1e">0<span class="blank _14"> </span>0<span class="blank _29"> </span>0 1<span class="blank _2a"> </span>0<span class="blank _2b"> </span>1<span class="blank _2c"> </span>0 1 2<span class="blank _14"> </span>0<span class="blank _2b"> </span>1<span class="blank _2d"> </span>2<span class="blank _29"> </span>0 1 2<span class="blank _2e"> </span>3</div><div class="t m8 x33 h18 y25 ff2 fs9 fc0 sc0 ls7 ws1f">0<span class="blank _2b"> </span>1<span class="blank _2f"> </span>1<span class="blank _2c"> </span>0 1</div><div class="c x34 y26 wb h19"><div class="t m9 x7 h1a y27 ff2 fsa fc0 sc0 ls7 ws20">(<span class="blank _30"> </span>)<span class="blank _31"> </span>[<span class="blank _2e"> </span>] (<span class="blank _32"> </span>)<span class="blank _18"> </span>[<span class="blank _2e"> </span>,<span class="blank _33"> </span>] (<span class="blank _34"> </span>)(<span class="blank _35"> </span>)<span class="blank _18"> </span>[<span class="blank _2e"> </span>, ,<span class="blank _36"> </span>] (<span class="blank _34"> </span>)(<span class="blank _35"> </span>)(<span class="blank _34"> </span>)<span class="blank _18"> </span>[<span class="blank _37"> </span>,<span class="blank _33"> </span>,<span class="blank _36"> </span>,<span class="blank _2e"> </span>]<span class="blank _1b"> </span>...</div></div><div class="t m9 x25 h1a y28 ff2 fsa fc0 sc0 ls7 ws21">(<span class="blank _34"> </span>)(<span class="blank _35"> </span>)<span class="blank _38"> </span>...<span class="blank _38"> </span>(<span class="blank _12"> </span>)<span class="blank _18"> </span>[<span class="blank _33"> </span>,<span class="blank _36"> </span>, ... ,<span class="blank _36"> </span>]</div><div class="t m8 x35 h1b y24 ff3 fs9 fc0 sc0 ls7">n</div><div class="t m8 x12 h1b y25 ff3 fs9 fc0 sc0 ls7 ws22">n n</div><div class="t m9 x25 h1c y29 ff3 fsa fc0 sc0 ls7 ws23">P<span class="blank _18"> </span>x<span class="blank _23"> </span>f<span class="blank _39"> </span>x<span class="blank _29"> </span>x x f<span class="blank _39"> </span>x<span class="blank _3a"> </span>x<span class="blank _3b"> </span>x x<span class="blank _3c"> </span>x x<span class="blank _3d"> </span>f<span class="blank _39"> </span>x<span class="blank _19"> </span>x<span class="blank _3e"> </span>x<span class="blank _29"> </span>x x<span class="blank _3c"> </span>x x<span class="blank _36"> </span>x x f<span class="blank _39"> </span>x<span class="blank _3a"> </span>x<span class="blank _3e"> </span>x<span class="blank _19"> </span>x</div><div class="t m9 x35 h1c y28 ff3 fsa fc0 sc0 ls7 ws24">x x<span class="blank _3c"> </span>x x<span class="blank _32"> </span>x x<span class="blank _3f"> </span>f<span class="blank _39"> </span>x<span class="blank _19"> </span>x<span class="blank _2c"> </span>x</div><div class="t m8 x36 h1d y25 ff4 fs9 fc0 sc0 ls7">−</div><div class="c x37 y2a wc h1e"><div class="t m9 x7 h1f y2b ff4 fsa fc0 sc0 ls7 ws25">=<span class="blank _1d"> </span>+ −<span class="blank _17"> </span>+ −<span class="blank _40"> </span>−<span class="blank _41"> </span>+ −<span class="blank _26"> </span>−<span class="blank _42"> </span>−<span class="blank _43"> </span>+<span class="blank _e"> </span>+</div></div><div class="t m9 x22 h1f y28 ff4 fsa fc0 sc0 ls7 ws26">− −<span class="blank _13"> </span>−</div><div class="t m1 x38 hd y2c ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 hd y2d ff2 fs1 fc0 sc0 ls7 ws6c">O erro é dado por </div><div class="t m1 x3 hd y2e ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t ma x39 h20 y2f ff2 fsb fc0 sc0 ls7 ws27">0<span class="blank _44"> </span>1<span class="blank _45"> </span>0 1 2</div><div class="c x3a y30 wd h5"><div class="t m6 x7 h21 y31 ff2 fsc fc0 sc0 ls7 ws28">(<span class="blank _1f"> </span>)<span class="blank _23"> </span>(<span class="blank _5"> </span>)(<span class="blank _1d"> </span>) ... (<span class="blank _5"> </span>)<span class="blank _46"> </span>[<span class="blank _36"> </span>,<span class="blank _36"> </span>,<span class="blank _47"> </span>,<span class="blank _48"> </span>...<span class="blank _38"> </span>,<span class="blank _47"> </span>,<span class="blank _19"> </span>]</div></div><div class="t ma x26 h22 y2f ff3 fsb fc0 sc0 ls7 ws29">n<span class="blank _49"> </span>n n</div><div class="c x3b y30 we h5"><div class="t m6 x7 h23 y31 ff3 fsc fc0 sc0 ls7 ws2a">R<span class="blank _37"> </span>x<span class="blank _4a"> </span>x x<span class="blank _e"> </span>x x<span class="blank _c"> </span>x x<span class="blank _10"> </span>f<span class="blank _3e"> </span>x<span class="blank _37"> </span>x<span class="blank _3a"> </span>x<span class="blank _5"> </span>x<span class="blank _2e"> </span>x</div></div><div class="t mb x25 h24 y2e ff4 fsd fc0 sc0 ls7">ε</div><div class="t m6 x34 h25 y2e ff4 fsc fc0 sc0 ls7 ws2b">=<span class="blank _14"> </span>= −<span class="blank _12"> </span>−<span class="blank _27"> </span>−<span class="blank _4b"> </span>×</div><div class="t m1 x3c hd y2e ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y32 ff1 fs1 fc0 sc0 ls7 ws6c">Fórmula de Newton-Gregory </div><div class="t m8 x3d h26 y33 ff2 fse fc0 sc0 ls7 ws2c">1 2<span class="blank _4c"> </span>3</div><div class="t m8 x3e h26 y34 ff2 fse fc0 sc0 ls7 ws2d">0 0<span class="blank _4c"> </span>0</div><div class="t m8 x3f h26 y35 ff2 fse fc0 sc0 ls7 ws2e">0<span class="blank _13"> </span>0<span class="blank _4d"> </span>0 1<span class="blank _4e"> </span>0 1 2</div><div class="t m8 x40 h26 y36 ff2 fse fc0 sc0 ls7 ws2f">2 3</div><div class="t m8 x41 h26 y37 ff2 fse fc0 sc0 ls7">0</div><div class="t m8 x42 h26 y38 ff2 fse fc0 sc0 ls7 ws30">0 1<span class="blank _2f"> </span>1</div><div class="t m8 x43 h27 y39 ff2 fsf fc0 sc0 ls7 ws31">( )<span class="blank _4f"> </span>( )<span class="blank _50"> </span>( )</div><div class="c x44 y3a wf h19"><div class="t m8 x7 h27 y3b ff2 fsf fc0 sc0 ls7 ws32">(<span class="blank _30"> </span>)<span class="blank _46"> </span>(<span class="blank _37"> </span>)<span class="blank _37"> </span>( )<span class="blank _b"> </span>( )<span class="blank _21"></span>(<span class="blank _35"> </span>)<span class="blank _51"> </span>( )(<span class="blank _35"> </span>)( )<span class="blank _2f"> </span>...</div></div><div class="t m8 x45 h27 y3c ff2 fsf fc0 sc0 ls7 ws33">2 !<span class="blank _52"> </span>3!</div><div class="t m8 x46 h27 y3d ff2 fsf fc0 sc0 ls7 ws34">( )</div><div class="t m8 x47 h27 y3e ff2 fsf fc0 sc0 ls7 ws35">(<span class="blank _34"> </span>)(<span class="blank _35"> </span>) ... (<span class="blank _12"> </span>)</div><div class="c x36 y3f w10 h28"><div class="t m8 x7 h27 y40 ff2 fsf fc0 sc0 ls7">!</div></div><div class="t m8 x48 h29 y35 ff3 fse fc0 sc0 ls7">n</div><div class="t m8 xc h29 y41 ff3 fse fc0 sc0 ls7">n</div><div class="t m8 x49 h29 y38 ff3 fse fc0 sc0 ls4">n<span class="ls7 v4">n</span></div><div class="t m8 x4a h2a y39 ff3 fsf fc0 sc0 ls7 ws36">f x<span class="blank _53"> </span>f x<span class="blank _54"> </span>f x</div><div class="t m8 x47 h2a y42 ff3 fsf fc0 sc0 ls7 ws37">P<span class="blank _18"> </span>x<span class="blank _23"> </span>f<span class="blank _1f"> </span>x<span class="blank _55"> </span>x x<span class="blank _56"> </span>x x<span class="blank _3c"> </span>x x<span class="blank _56"> </span>x x<span class="blank _3c"> </span>x x<span class="blank _36"> </span>x x</div><div class="t m8 x2d h2a y3c ff3 fsf fc0 sc0 ls7 ws38">h h<span class="blank _57"> </span>h</div><div class="t m8 xd h2a y3d ff3 fsf fc0 sc0 ls7 ws39">f x</div><div class="t m8 x48 h2a y3e ff3 fsf fc0 sc0 ls7 ws3a">x x<span class="blank _3c"> </span>x x<span class="blank _32"> </span>x x</div><div class="c x6 y3f w11 h28"><div class="t m8 x7 h2a y40 ff3 fsf fc0 sc0 ls7 ws3b">h n</div></div><div class="t m8 x4b h2b y38 ff4 fse fc0 sc0 ls7">−</div><div class="t m8 x13 h2c y39 ff4 fsf fc0 sc0 ls7 ws3c">∆ ∆<span class="blank _58"> </span>∆</div><div class="c x4c y43 w12 h2d"><div class="t m8 x7 h2c y44 ff4 fsf fc0 sc0 ls7 ws3d">=<span class="blank _5"> </span>+<span class="blank _47"> </span>−<span class="blank _59"> </span>+<span class="blank _5a"> </span>− −<span class="blank _59"> </span>+<span class="blank _5a"> </span>− −<span class="blank _34"> </span>−<span class="blank _5b"> </span>+<span class="blank _e"> </span>+</div></div><div class="t m8 x2d h2c y3d ff4 fsf fc0 sc0 ls7">∆</div><div class="t m8 x4d h2c y3e ff4 fsf fc0 sc0 ls7 ws3e">− −<span class="blank _13"> </span>−</div><div class="t m1 x4e hd y45 ff2 fs1 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y46 ff1 fs1 fc0 sc0 ls7 ws6c">Método de mínimos quadrados </div><div class="t m1 x15 hd y47 ff2 fs1 fc0 sc0 ls7 ws6c">Sendo <span class="blank _5c"> </span> <span class="blank _5c"> </span><span class="ff3 wse">p=a</span></div><div class="t m4 x4f he y48 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x13 hf y47 ff3 fs1 fc0 sc0 ls7">u</div><div class="t m4 x3d he y48 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x9 hf y47 ff3 fs1 fc0 sc0 ls7 wse">+a</div><div class="t m4 x3e he y48 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x39 hf y47 ff3 fs1 fc0 sc0 ls7">u</div><div class="t m4 x12 he y48 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x50 hf y47 ff3 fs1 fc0 sc0 ls7 ws6c">+ <span class="blank _5c"> </span>... <span class="blank _5c"> </span>+ <span class="blank _5c"> </span>a</div><div class="t m4 x51 he y48 ff3 fs4 fc0 sc0 ls7">m</div><div class="t m1 x30 hf y47 ff3 fs1 fc0 sc0 ls7">u</div><div class="t m4 x18 he y48 ff3 fs4 fc0 sc0 ls7">m</div><div class="t m1 x52 hd y47 ff2 fs1 fc0 sc0 ls7 ws6c">, <span class="blank _5c"> </span>temos <span class="blank _5c"> </span>que <span class="blank _5c"> </span>os <span class="blank _5c"> </span>coeficientes <span class="blank _5c"> </span><span class="ff3">a</span></div><div class="t m4 x53 he y48 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x54 hf y47 ff3 fs1 fc0 sc0 ls7 wse">,a</div><div class="t m4 x55 he y48 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x56 hf y47 ff3 fs1 fc0 sc0 ls7 wse">,a</div><div class="t m4 x57 he y48 ff3 fs4 fc0 sc0 ls7">2</div><div class="t m1 x58 hf y47 ff3 fs1 fc0 sc0 ls7 ws6c">, <span class="blank _5c"> </span>... <span class="blank _5c"> </span>,a</div><div class="t m4 x59 he y48 ff3 fs4 fc0 sc0 ls7">m</div><div class="t m1 x5a hd y47 ff3 fs1 fc0 sc0 ls5 ws6c"> <span class="ff2 ls7">do <span class="blank _5c"> </span>polinômio </span></div><div class="t m1 x3 hd y49 ff2 fs1 fc0 sc0 ls7 ws6c">procurado são então dados pelo sistema linear normal: </div><div class="c x5b y4a w13 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">(</div></div><div class="c x5c y4a w14 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">)</div></div><div class="c x5d y4a w13 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">(</div></div><div class="c x5e y4a w14 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">)</div></div><div class="c x3e y4a w13 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">(</div></div><div class="c x5f y4a w14 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">)</div></div><div class="t mc x5b h2f y4c ff4 fs10 fc0 sc0 ls7 ws3f">(<span class="blank _6"> </span>) (<span class="blank _7"> </span>)<span class="blank _5d"> </span>(<span class="blank _13"> </span>)</div><div class="t mc x48 h2f y4d ff4 fs10 fc0 sc0 ls7 ws40">(<span class="blank _27"> </span>) (<span class="blank _5e"> </span>)<span class="blank _5f"> </span>(<span class="blank _16"> </span>)</div><div class="c x1a y4a w13 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">(</div></div><div class="c x1d y4a w14 h2e"><div class="t mc x7 h2f y4b ff4 fs10 fc0 sc0 ls7">)</div></div><div class="t mc x60 h2f y4c ff4 fs10 fc0 sc0 ls7 ws41">( )</div><div class="t mc x1a h2f y4d ff4 fs10 fc0 sc0 ls7 ws42">( )</div><div class="t md x61 h30 y4e ff2 fs11 fc0 sc0 ls7 ws43">0<span class="blank _3c"> </span>0<span class="blank _60"> </span>1 0<span class="blank _61"> </span>0<span class="blank _2b"> </span>0<span class="blank _9"> </span>0</div><div class="t md x61 h30 y4f ff2 fs11 fc0 sc0 ls7 ws44">0<span class="blank _36"> </span>1<span class="blank _12"> </span>1 1<span class="blank _61"> </span>1<span class="blank _2b"> </span>1<span class="blank _9"> </span>1</div><div class="t md x61 h30 y50 ff2 fs11 fc0 sc0 ls7 ws45">0 1</div><div class="t m2 x42 h31 y51 ff2 fs12 fc0 sc0 ls7 ws46">, ,<span class="blank _62"> </span>,<span class="blank _63"> </span>,</div><div class="t m2 x42 h31 y52 ff2 fs12 fc0 sc0 ls7 ws46">, ,<span class="blank _62"> </span>,<span class="blank _63"> </span>,</div><div class="t m2 x0 h31 y53 ff2 fs12 fc0 sc0 ls7 ws46">, ,<span class="blank _62"> </span>,<span class="blank _63"> </span>,</div><div class="t md x62 h32 y4e ff3 fs11 fc0 sc0 ls7">m</div><div class="t md x62 h32 y4f ff3 fs11 fc0 sc0 ls7">m</div><div class="t md x63 h32 y50 ff3 fs11 fc0 sc0 ls7 ws47">m<span class="blank _15"> </span>m<span class="blank _64"> </span>m m<span class="blank _4a"> </span>m<span class="blank _5d"> </span>m</div><div class="t m2 x4d h33 y51 ff3 fs12 fc0 sc0 ls7 ws48">u<span class="blank _33"> </span>u<span class="blank _2b"> </span>u<span class="blank _3e"> </span>u<span class="blank _1"> </span>u<span class="blank _65"> </span>u<span class="blank _26"> </span>a<span class="blank _14"> </span>y u</div><div class="c x64 y54 w15 h5"><div class="t m2 x7 h33 y55 ff3 fs12 fc0 sc0 ls7 ws49">u<span class="blank _33"> </span>u<span class="blank _2b"> </span>u<span class="blank _3e"> </span>u<span class="blank _1"> </span>u<span class="blank _65"> </span>u<span class="blank _26"> </span>a<span class="blank _14"> </span>y u</div></div><div class="t m2 x4d h33 y53 ff3 fs12 fc0 sc0 ls7 ws48">u<span class="blank _33"> </span>u<span class="blank _2b"> </span>u<span class="blank _3e"> </span>u<span class="blank _1"> </span>u<span class="blank _65"> </span>u<span class="blank _26"> </span>a<span class="blank _14"> </span>y u</div><div class="c x47 y56 w16 h34"><div class="t m2 x7 h35 y57 ff4 fs12 fc0 sc0 ls7 ws4a"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y58 ff4 fs12 fc0 sc0 ls7 ws4b"> </div><div class="c x47 y59 w16 h34"><div class="t m2 x7 h35 y5a ff4 fs12 fc0 sc0 ls7 ws4c"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y5b ff4 fs12 fc0 sc0 ls7 ws4d"> </div><div class="c x47 y5c w16 h34"><div class="t m2 x7 h35 y5d ff4 fs12 fc0 sc0 ls7 ws4c"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y5e ff4 fs12 fc0 sc0 ls7 ws4e"><span class="blank _3f"> </span> <span class="v5">=</span></div><div class="c x47 y5f w16 h34"><div class="t m2 x7 h35 y60 ff4 fs12 fc0 sc0 ls7 ws4c"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y61 ff4 fs12 fc0 sc0 ls7 ws4d"> </div><div class="c x47 y62 w16 h34"><div class="t m2 x7 h35 y63 ff4 fs12 fc0 sc0 ls7 ws4c"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y64 ff4 fs12 fc0 sc0 ls7 ws4d"> </div><div class="c x47 y65 w16 h34"><div class="t m2 x7 h35 y66 ff4 fs12 fc0 sc0 ls7 ws4c"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x16 h35 y67 ff4 fs12 fc0 sc0 ls7 ws4b"> </div><div class="c x47 y68 w16 h34"><div class="t m2 x7 h35 y69 ff4 fs12 fc0 sc0 ls7 ws4a"><span class="blank _66"> </span><span class="blank _67"> </span> </div></div><div class="t m2 x4b h36 y51 ff5 fs12 fc0 sc0 ls7">⋯</div><div class="t m2 x4b h36 y52 ff5 fs12 fc0 sc0 ls7">⋯</div><div class="t m2 x42 h36 y6a ff5 fs12 fc0 sc0 ls7 ws4f">⋮<span class="blank _5f"> </span>⋮ ⋮<span class="blank _44"> </span>⋮<span class="blank _6"> </span>⋮<span class="blank _68"> </span>⋮</div><div class="t m2 x4b h36 y53 ff5 fs12 fc0 sc0 ls7">⋯</div><div class="t m2 x65 h31 y6b ff2 fs12 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y6c ff1 fs1 fc0 sc0 ls7 ws6c">Caso contínuo - </div><div class="t me x5e h37 y6d ff4 fs13 fc0 sc0 ls7 ws50">( )</div><div class="c x13 y6e w17 h5"><div class="t m1 x7 h38 y6f ff2 fs14 fc0 sc0 ls7 ws51">,<span class="blank _69"> </span>( )<span class="blank _19"> </span>( )</div></div><div class="t md x39 h39 y70 ff3 fs15 fc0 sc0 ls7">b</div><div class="t md x39 h39 y71 ff3 fs15 fc0 sc0 ls7">a</div><div class="c x66 y6e w18 h5"><div class="t m1 x67 h3a y6f ff3 fs14 fc0 sc0 ls7 ws52">f g<span class="blank _2b"> </span>f x<span class="blank _6a"> </span>g<span class="blank _39"> </span>x<span class="blank _6b"> </span>dx</div></div><div class="t m1 x68 h3b y6c ff4 fs14 fc0 sc0 ls7">=</div><div class="t mf x39 h3c y72 ff4 fs16 fc0 sc0 ls7">∫</div><div class="t m1 x18 h38 y6c ff2 fs14 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 y73 ff1 fs1 fc0 sc0 ls7 ws6c">Erro de truncamento </div><div class="t m10 x13 h3d y74 ff4 fs17 fc0 sc0 ls7 ws53">[ ]</div><div class="c x2 y75 w19 h3e"><div class="t md x7 h3f y76 ff2 fs15 fc0 sc0 ls7">2</div></div><div class="t md xb h3f y77 ff2 fs15 fc0 sc0 ls7">2</div><div class="c x15 y78 w1a h5"><div class="t m1 x7 h38 y79 ff2 fs14 fc0 sc0 ls7 ws54">( )<span class="blank _41"> </span>(<span class="blank _3c"> </span>)<span class="blank _c"> </span>(<span class="blank _65"> </span>)</div></div><div class="t md x69 h39 y7a ff3 fs15 fc0 sc0 ls7">b</div><div class="t md x26 h39 y7b ff3 fs15 fc0 sc0 ls7 ws55">m<span class="blank _6c"> </span>k<span class="blank _35"> </span>m k</div><div class="t md x69 h39 y7c ff3 fs15 fc0 sc0 ls7">a</div><div class="t m1 x47 h3b y7d ff3 fs14 fc0 sc0 ls7 ws52">Q<span class="blank _4b"> </span>f<span class="blank _19"> </span>x<span class="blank _3f"> </span>P<span class="blank _a"> </span>f x<span class="blank _29"> </span>P<span class="blank _2e"> </span>x<span class="blank _6d"></span><span class="ff4 ws56">=<span class="blank _44"> </span>− =<span class="blank _6e"> </span>−</span></div><div class="t mf x69 h3c y7e ff4 fs16 fc0 sc0 ls7">∫</div><div class="t m1 x6a h38 y7d ff2 fs14 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y7f ff1 fs1 fc0 sc0 ls7 ws6c">Caso discreto - </div><div class="t m11 x8 h40 y80 ff4 fs18 fc0 sc0 ls7 ws57">( )</div><div class="t md x39 h3f y81 ff2 fs15 fc0 sc0 ls7">1</div><div class="t m1 x69 h38 y82 ff2 fs14 fc0 sc0 ls7">,</div><div class="t md x3e h39 y83 ff3 fs15 fc0 sc0 ls7">n</div><div class="c x5 y84 w1b h8"><div class="t md x7 h39 y85 ff3 fs15 fc0 sc0 ls7 ws58">i i</div></div><div class="t md x31 h39 y81 ff3 fs15 fc0 sc0 ls7">i</div><div class="c x5e y86 w1c h5"><div class="t m1 x7 h3a y87 ff3 fs14 fc0 sc0 ls7 ws59">x<span class="blank _30"> </span>y<span class="blank _7"> </span>x y</div></div><div class="t m5 x3e h16 y81 ff4 fs6 fc0 sc0 ls7">=</div><div class="t m1 x4a h3b y82 ff4 fs14 fc0 sc0 ls7">=</div><div class="c x6 y88 w1d h41"><div class="t mf x7 h3c y89 ff4 fs16 fc0 sc0 ls7">∑</div></div><div class="t m1 x6b h38 y7f ff2 fs14 fc0 sc0 ls7 ws6c">, onde <span class="ff3 ws5a">x=(x</span></div><div class="t m4 x6c he y80 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x6d h3a y7f ff3 fs14 fc0 sc0 ls7 ws5a">,x</div><div class="t m4 x2c he y80 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 xa h3a y7f ff3 fs14 fc0 sc0 ls7 ws5a">,x</div><div class="t m4 x6e he y80 ff3 fs4 fc0 sc0 ls7">2</div><div class="t m1 x6f h3a y7f ff3 fs14 fc0 sc0 ls6 ws6c">, ... ,x</div><div class="t m4 x70 he y80 ff3 fs4 fc0 sc0 ls7">n</div><div class="t m1 x1e h3a y7f ff3 fs14 fc0 sc0 ls7">)</div><div class="t m4 x1f he y8a ff3 fs4 fc0 sc0 ls7">t</div><div class="t m1 x71 h38 y7f ff2 fs14 fc0 sc0 ls7 ws6c"> e <span class="ff3 ws5a">y=(y</span></div><div class="t m4 x2f he y80 ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x72 h3a y7f ff3 fs14 fc0 sc0 ls7 ws5a">,y</div><div class="t m4 x73 he y80 ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x74 h3a y7f ff3 fs14 fc0 sc0 ls7 ws5a">,y</div><div class="t m4 x75 he y80 ff3 fs4 fc0 sc0 ls7">2</div><div class="t m1 x76 h3a y7f ff3 fs14 fc0 sc0 ls6 ws6c">, ... ,y</div><div class="t m4 x56 he y80 ff3 fs4 fc0 sc0 ls7">n</div><div class="t m1 x77 h3a y7f ff3 fs14 fc0 sc0 ls7">)</div><div class="t m4 x32 he y8a ff3 fs4 fc0 sc0 ls7">t</div><div class="t m1 x78 h38 y7f ff2 fs14 fc0 sc0 ls7 ws6c">. </div><div class="t m1 x15 h3 y8b ff1 fs1 fc0 sc0 ls7 ws6c">Erro de truncamento </div><div class="t m12 x3d h42 y8c ff4 fs19 fc0 sc0 ls7 ws5b">[ ]</div><div class="c x6a y8d w1e h3e"><div class="t md x7 h3f y8e ff2 fs15 fc0 sc0 ls7">2</div></div><div class="t md xb h3f y8f ff2 fs15 fc0 sc0 ls7">2</div><div class="t md x4b h3f y90 ff2 fs15 fc0 sc0 ls7">0</div><div class="c x15 y91 w1f h5"><div class="t m1 x7 h38 y92 ff2 fs14 fc0 sc0 ls7 ws5c">(<span class="blank _1f"> </span>)<span class="blank _6f"> </span>( )<span class="blank _c"> </span>( )</div></div><div class="t md x49 h39 y93 ff3 fs15 fc0 sc0 ls7">n</div><div class="t md x26 h39 y94 ff3 fs15 fc0 sc0 ls7 ws5d">m<span class="blank _70"> </span>k<span class="blank _35"> </span>m k</div><div class="t md x69 h39 y90 ff3 fs15 fc0 sc0 ls7">k</div><div class="t m1 x47 h3a y95 ff3 fs14 fc0 sc0 ls7 ws5e">Q<span class="blank _4b"> </span>f x<span class="blank _3f"> </span>P<span class="blank _71"> </span>f x<span class="blank _29"> </span>P<span class="blank _37"> </span>x</div><div class="t m5 x49 h16 y90 ff4 fs6 fc0 sc0 ls7">=</div><div class="t m1 x64 h3b y95 ff4 fs14 fc0 sc0 ls7 ws5f">=<span class="blank _44"> </span>− =<span class="blank _6c"> </span>−</div><div class="t mf x69 h3c y96 ff4 fs16 fc0 sc0 ls7">∑</div><div class="t m1 x79 h38 y97 ff2 fs14 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y98 ff1 fs1 fc0 sc0 ls7 ws6c">Outros tipos de aproximações </div><div class="t m1 x15 h38 y99 ff2 fs14 fc0 sc0 ls7 ws6c">O <span class="blank _0"> </span>objetivo <span class="blank _0"> </span>dos <span class="blank _72"> </span>métodos <span class="blank _0"> </span>dos <span class="blank _0"> </span>m<span class="blank _0"> </span>ínimos <span class="blank _0"> </span>quadrados <span class="blank _0"> </span>é <span class="blank _0"> </span>aprox<span class="blank _0"> </span>imar <span class="blank _0"> </span>a <span class="blank _0"> </span>função <span class="blank _0"> </span>da<span class="blank _0"> </span>da <span class="blank _0"> </span>por <span class="blank _0"> </span>uma <span class="blank _72"> </span>família </div><div class="t m1 x3 h38 y9a ff2 fs14 fc0 sc0 ls7 ws6c">linear nos parâmetros, definida por ex<span class="blank _0"> </span>pressões da forma: </div><div class="t m1 x15 h3a y9b ff3 fs14 fc0 sc0 ls7">a</div><div class="t m4 x35 he y9c ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x34 h3a y9b ff3 fs14 fc0 sc0 ls7">g</div><div class="t m4 x7a he y9c ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x5d h3a y9b ff3 fs14 fc0 sc0 ls7 ws6c">(x) +<span class="blank _21"></span> a</div><div class="t m4 x66 he y9c ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x69 h3a y9b ff3 fs14 fc0 sc0 ls7">g</div><div class="t m4 x13 he y9c ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x7b h3a y9b ff3 fs14 fc0 sc0 ls7 ws6c">(x) + ... + a</div><div class="t m4 x7c he y9c ff3 fs4 fc0 sc0 ls7">m</div><div class="t m1 x7d h3a y9b ff3 fs14 fc0 sc0 ls7">g</div><div class="t m4 x7e he y9c ff3 fs4 fc0 sc0 ls7">m</div><div class="t m1 x2 h3a y9b ff3 fs14 fc0 sc0 ls7 ws6c">(x) </div><div class="t m1 x15 h38 y9d ff2 fs14 fc0 sc0 ls7 ws6c">Assim <span class="ff3">a</span></div><div class="t m4 xb he y9e ff3 fs4 fc0 sc0 ls7">0</div><div class="t m1 x23 h38 y9d ff2 fs14 fc0 sc0 ls7 ws6c"> e <span class="ff3">a</span></div><div class="t m4 x49 he y9e ff3 fs4 fc0 sc0 ls7">1</div><div class="t m1 x4b h38 y9d ff2 fs14 fc0 sc0 ls7 ws6c"> são solução do sistema linear normal. </div><div class="t m5 x61 h43 y9f ff2 fs1a fc0 sc0 ls7 ws60">0<span class="blank _2d"> </span>0<span class="blank _73"> </span>1 0<span class="blank _2"> </span><span class="ws61 v0">0 0</span></div><div class="t m5 x61 h43 ya0 ff2 fs1a fc0 sc0 ls7 ws62">0<span class="blank _2b"> </span>1<span class="blank _68"> </span>1 1<span class="blank _2"> </span><span class="ws63 v0">1 1</span></div><div class="t m8 x5b h44 ya1 ff2 fs1b fc0 sc0 ls7 ws64">(<span class="blank _47"> </span>( ),<span class="blank _e"> </span>( )<span class="blank _21"></span>)<span class="blank _74"> </span>(<span class="blank _65"> </span>( ),<span class="blank _e"> </span>( ))</div><div class="c x7f ya2 w20 h5"><div class="t m8 x7 h44 ya3 ff2 fs1b fc0 sc0 ls7 ws65">(<span class="blank _37"> </span>( ),<span class="blank _e"> </span>( ))</div></div><div class="t m8 x5b h44 ya4 ff2 fs1b fc0 sc0 ls7 ws64">(<span class="blank _47"> </span>( ),<span class="blank _47"> </span>( ))<span class="blank _5a"> </span>(<span class="blank _65"> </span>( ),<span class="blank _47"> </span>( ))</div><div class="c x7f ya5 w21 h5"><div class="t m8 x7 h44 ya6 ff2 fs1b fc0 sc0 ls7 ws65">(<span class="blank _37"> </span>( ),<span class="blank _47"> </span>( ))</div></div><div class="t m8 x4d h45 ya1 ff3 fs1b fc0 sc0 ls7 ws66">g<span class="blank _1b"> </span>x g<span class="blank _36"> </span>x<span class="blank _42"> </span>g x g<span class="blank _1b"> </span>x</div><div class="c x80 ya2 w22 h5"><div class="t m8 x7 h45 ya3 ff3 fs1b fc0 sc0 ls7 ws67">a<span class="blank _1a"> </span>F x<span class="blank _37"> </span>g<span class="blank _1b"> </span>x</div></div><div class="t m8 x4d h45 ya4 ff3 fs1b fc0 sc0 ls7 ws66">g<span class="blank _1b"> </span>x g x<span class="blank _4a"> </span>g<span class="blank _33"> </span>x g<span class="blank _33"> </span>x</div><div class="c x80 ya5 w23 h5"><div class="t m8 x7 h45 ya6 ff3 fs1b fc0 sc0 ls7 ws67">a<span class="blank _1a"> </span>F x<span class="blank _37"> </span>g<span class="blank _33"> </span>x</div></div><div class="t m8 x47 h46 ya7 ff4 fs1b fc0 sc0 ls7 ws68"> </div><div class="c x5f ya8 w24 h34"><div class="t m8 x7 h46 ya9 ff4 fs1b fc0 sc0 ls7 ws69"><span class="blank _e"> </span> <span class="blank _75"> </span></div></div><div class="t m8 x2b h46 yaa ff4 fs1b fc0 sc0 ls7">=</div><div class="t m8 x47 h46 yab ff4 fs1b fc0 sc0 ls7 ws6a"> </div><div class="c x5f yac w24 h34"><div class="t m8 x7 h46 yad ff4 fs1b fc0 sc0 ls7 ws6b"><span class="blank _e"> </span> <span class="blank _75"> </span></div></div><div class="c x5f yae w24 h34"><div class="t m8 x7 h46 yaf ff4 fs1b fc0 sc0 ls7 ws69"><span class="blank _e"> </span> <span class="blank _75"> </span></div></div><div class="t m8 x47 h46 yb0 ff4 fs1b fc0 sc0 ls7 ws68"> </div><div class="t m1 x81 h38 yaa ff2 fs14 fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h38 yb1 ff2 fs14 fc0 sc0 ls7 ws6c"> </div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 yb2 w25 h47" alt src="https://files.passeidireto.com/e228eb14-7ade-4ad5-bff0-d10d2cb7b2eb/bg2.png" alt="Pré-visualização de imagem de arquivo"><div class="t m13 x7d h48 yb3 ff2 fs1c fc0 sc0 ls7 ws6c">Integração Numérica </div><div class="t m13 x82 h48 yb4 ff2 fs1c fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 yb5 ff1 fs1 fc0 sc0 ls7 ws6c">Fórmulas de Quadraturas Interpolatória </div><div class="t m14 x1 h49 yb6 ff2 fs1d fc0 sc0 ls7">0</div><div class="c x22 yb7 w26 h4a"><div class="t m15 x7 h4b yb8 ff2 fs1e fc0 sc0 ls7 ws6d">( )<span class="blank _76"> </span>( )</div></div><div class="t m14 x23 h4c yb9 ff3 fs1d fc0 sc0 ls7">n</div><div class="t m14 x24 h4c yba ff3 fs1d fc0 sc0 ls7 ws6e">n<span class="blank _9"> </span>k k</div><div class="t m14 xb h4c yb6 ff3 fs1d fc0 sc0 ls7">k</div><div class="c x25 yb7 w27 h4a"><div class="t m15 x7 h4d yb8 ff3 fs1e fc0 sc0 ls7 ws6f">P<span class="blank _19"> </span>x<span class="blank _1a"> </span>f l<span class="blank _1b"> </span>x</div></div><div class="t m14 x23 h4e yb6 ff4 fs1d fc0 sc0 ls7">=</div><div class="t m15 x26 h4f ybb ff4 fs1e fc0 sc0 ls7">=</div><div class="t m3 xb h50 ybc ff4 fs1f fc0 sc0 ls7">∑</div><div class="t m15 xd h4b ybd ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 ybe ff1 fs1 fc0 sc0 ls7 ws6c">Fórmula de Newton-Cotes </div><div class="t m1 x15 h3 ybf ff1 fs1 fc0 sc0 ls7 ws6c">Regra do Trapézio</div><div class="t m15 x12 h4b ybf ff2 fs1e fc0 sc0 ls7 ws6c">. - </div><div class="t m16 x83 h51 yc0 ff2 fs20 fc0 sc0 ls7">1</div><div class="t m16 x83 h51 yc1 ff2 fs20 fc0 sc0 ls7">0</div><div class="t m17 x84 h52 yc2 ff2 fs21 fc0 sc0 ls7 ws70">0 1</div><div class="t mf x29 h53 yc3 ff2 fs22 fc0 sc0 ls7 ws71">1 1</div><div class="c x7d yc4 w28 h54"><div class="t mf x7 h53 yc5 ff2 fs22 fc0 sc0 ls7 ws72">( )<span class="blank _77"> </span>(<span class="blank _3c"> </span>)<span class="blank _78"> </span>(<span class="blank _1b"> </span>)</div></div><div class="t mf x29 h53 yc6 ff2 fs22 fc0 sc0 ls7 ws71">2 2</div><div class="t m17 x4 h55 yc7 ff3 fs21 fc0 sc0 ls7">x</div><div class="t m17 x4 h55 yc8 ff3 fs21 fc0 sc0 ls7">x</div><div class="c x5f yc4 w29 h54"><div class="t mf x67 h56 yc5 ff3 fs22 fc0 sc0 ls7 ws73">f x<span class="blank _79"> </span>dx<span class="blank _2e"> </span>h<span class="blank _29"> </span>f x<span class="blank _7a"> </span>f x</div></div><div class="c x1a yc9 w2a h57"><div class="t mf x7 h58 y15 ff4 fs22 fc0 sc0 ls7 ws74"> </div></div><div class="t mf x85 h58 yca ff4 fs22 fc0 sc0 ls7">+</div><div class="c x1a ycb w2a h57"><div class="t mf x7 h58 ycc ff4 fs22 fc0 sc0 ls7 ws74"> </div></div><div class="c x1a ycd w2a h57"><div class="t mf x7 h58 yce ff4 fs22 fc0 sc0 ls7 ws74"> </div></div><div class="t m18 x4 h59 ycf ff4 fs23 fc0 sc0 ls7">∫</div><div class="t mf x7f h5a yca ff5 fs22 fc0 sc0 ls7">≃</div><div class="t m15 x72 h4b ybf ff2 fs1e fc0 sc0 ls7 ws6c"> ou </div><div class="t m19 x86 h5b yd0 ff4 fs24 fc0 sc0 ls7 ws75">[ ]</div><div class="t m14 x87 h5c yd1 ff2 fs25 fc0 sc0 ls7">1</div><div class="t m14 x87 h5c yd2 ff2 fs25 fc0 sc0 ls7">0</div><div class="c x88 yd3 w2b h5d"><div class="t m3 x7 h5e yd4 ff2 fs26 fc0 sc0 ls7 ws76">0 1</div></div><div class="c x89 yd5 w2c h5f"><div class="t m1a x7 h60 yd6 ff2 fs27 fc0 sc0 ls7 ws77">( )<span class="blank _64"> </span>(<span class="blank _3c"> </span>)<span class="blank _f"> </span>(<span class="blank _36"> </span>)</div></div><div class="t m1a x8a h60 yd7 ff2 fs27 fc0 sc0 ls7">2</div><div class="t m3 x75 h61 yd8 ff3 fs26 fc0 sc0 ls7">x</div><div class="t m3 x75 h61 yd9 ff3 fs26 fc0 sc0 ls7">x</div><div class="t m1a x8a h62 yda ff3 fs27 fc0 sc0 ls7">h</div><div class="c x8b yd5 w2d h5f"><div class="t m1a x67 h62 yd6 ff3 fs27 fc0 sc0 ls7 ws78">f x<span class="blank _79"> </span>dx<span class="blank _11"> </span>f x<span class="blank _34"> </span>f x</div></div><div class="t m1a x8c h63 ydb ff4 fs27 fc0 sc0 ls7">+</div><div class="t m1b x75 h64 ydc ff4 fs28 fc0 sc0 ls7">∫</div><div class="t m1a x8d h65 ydb ff5 fs27 fc0 sc0 ls7">≃</div><div class="t m15 x8e h4b ybf ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m15 x15 h4b ydd ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 yde ff1 fs1 fc0 sc0 ls7 ws6c">Regra </div><div class="c xe ydf w2e h54"><div class="t m1c x7 h66 ye0 ff2 fs29 fc0 sc0 ls7">1</div></div><div class="c xe ye1 w2f h67"><div class="t m1c x7 h66 ye2 ff2 fs29 fc0 sc0 ls7">3</div></div><div class="t m1 x8f h3 yde ff1 fs1 fc0 sc0 ls7 ws6c"> de Simpson. - </div><div class="t m1d x90 h68 ye3 ff4 fs2a fc0 sc0 ls7 ws79">[ ]</div><div class="t m14 x80 h5c ye4 ff2 fs25 fc0 sc0 ls7">2</div><div class="t m14 x80 h5c ye5 ff2 fs25 fc0 sc0 ls7">0</div><div class="t m17 x65 h52 ye6 ff2 fs21 fc0 sc0 ls7 ws7a">0<span class="blank _5f"> </span>1 2</div><div class="c x2 ye7 w30 h54"><div class="t mf x7 h53 ye8 ff2 fs22 fc0 sc0 ls7 ws7b">(<span class="blank _18"> </span>)<span class="blank _7b"> </span>( ) 4<span class="blank _33"> </span>(<span class="blank _36"> </span>)<span class="blank _10"> </span>( )</div></div><div class="t mf x29 h53 ye9 ff2 fs22 fc0 sc0 ls7">3</div><div class="t m17 x7c h55 yea ff3 fs21 fc0 sc0 ls7">x</div><div class="t m17 x7c h55 yeb ff3 fs21 fc0 sc0 ls7">x</div><div class="t mf x29 h56 yec ff3 fs22 fc0 sc0 ls7">h</div><div class="c x16 ye7 w31 h54"><div class="t mf x67 h56 ye8 ff3 fs22 fc0 sc0 ls7 ws7c">f x<span class="blank _79"> </span>dx<span class="blank _7c"> </span>f x<span class="blank _11"> </span>f x<span class="blank _35"> </span>f x</div></div><div class="t mf x91 h58 yed ff4 fs22 fc0 sc0 ls7 ws7d">+ +</div><div class="t m18 x7c h59 yee ff4 fs23 fc0 sc0 ls7">∫</div><div class="t mf x6c h5a yed ff5 fs22 fc0 sc0 ls7">≃</div><div class="t m15 x92 h4b yde ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 yef ff1 fs1 fc0 sc0 ls7 ws6c">Regra </div><div class="c xe yf0 w2f h54"><div class="t m1c x7 h66 yf1 ff2 fs29 fc0 sc0 ls7">3</div></div><div class="c xe yf2 w2e h67"><div class="t m1c x7 h66 yf3 ff2 fs29 fc0 sc0 ls7">8</div></div><div class="t m1 x8f h3 yef ff1 fs1 fc0 sc0 ls7 ws6c"> de Simpson. - </div><div class="t m15 x5f h4b yef ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1e x93 h68 yf4 ff4 fs2a fc0 sc0 ls7 ws7e">[ ]</div><div class="t m14 x7d h5c yf5 ff2 fs25 fc0 sc0 ls7">3</div><div class="t m14 x7d h5c yf6 ff2 fs25 fc0 sc0 ls7">0</div><div class="t m17 x94 h52 yf7 ff2 fs21 fc0 sc0 ls7 ws7f">0<span class="blank _68"> </span>1<span class="blank _68"> </span>2 3</div><div class="t mf x45 h53 yf8 ff2 fs22 fc0 sc0 ls7">3</div><div class="c x2b yf9 w32 h54"><div class="t mf x7 h53 yfa ff2 fs22 fc0 sc0 ls7 ws80">(<span class="blank _18"> </span>)<span class="blank _77"> </span>(<span class="blank _3c"> </span>) 3<span class="blank _33"> </span>(<span class="blank _1b"> </span>) 3<span class="blank _3d"> </span>(<span class="blank _47"> </span>)<span class="blank _10"> </span>( )</div></div><div class="t mf x45 h53 yfb ff2 fs22 fc0 sc0 ls7">8</div><div class="t m17 x80 h55 yfc ff3 fs21 fc0 sc0 ls7">x</div><div class="t m17 x80 h55 yfd ff3 fs21 fc0 sc0 ls7">x</div><div class="c x7e yf9 w33 h54"><div class="t mf x67 h56 yfa ff3 fs22 fc0 sc0 ls7 ws7c">f x<span class="blank _79"> </span>dx<span class="blank _7d"> </span>h f x<span class="blank _7c"> </span>f x<span class="blank _5"> </span>f x<span class="blank _32"> </span>f x</div></div><div class="t mf x95 h58 yfe ff4 fs22 fc0 sc0 ls7 ws81">+ +<span class="blank _7e"> </span>+</div><div class="t m18 x96 h59 yff ff4 fs23 fc0 sc0 ls7">∫</div><div class="t mf x1a h5a yfe ff5 fs22 fc0 sc0 ls7">≃</div><div class="t m15 x97 h4b yef ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1 x3 h3 y100 ff1 fs1 fc0 sc0 ls7 ws6c">Erros nas fórmulas de Newton-Cotes </div><div class="t m1 x15 h3 y101 ff1 fs1 fc0 sc0 ls7 ws6c">Erro na regra do trapézio - </div><div class="t m3 x1c h69 y102 ff2 fs2b fc0 sc0 ls7">3</div><div class="c x30 y103 w34 h5"><div class="t m15 x7 h4b y104 ff2 fs1e fc0 sc0 ls7 ws82">(<span class="blank _3d"> </span>)<span class="blank _a"> </span>max<span class="blank _e"> </span>'<span class="blank _21"></span>'<span class="blank _21"></span>( )</div></div><div class="c x98 y105 w35 h4a"><div class="t m15 x7 h4b y106 ff2 fs1e fc0 sc0 ls7 ws83">12</div></div><div class="t m3 x99 h6a y107 ff3 fs2b fc0 sc0 ls7 ws84">a t b</div><div class="t m15 x2c h4d y108 ff3 fs1e fc0 sc0 ls7 ws85">Nh</div><div class="c x2b y103 w36 h5"><div class="t m15 x7 h4d y104 ff3 fs1e fc0 sc0 ls7 ws86">R f<span class="blank _7f"> </span>f<span class="blank _3c"> </span>t</div></div><div class="t m3 x9a h6b y107 ff4 fs2b fc0 sc0 ls7 ws87">< <</div><div class="t m1 x1a h6c y101 ff4 fs1 fc0 sc0 ls7">≤</div><div class="t m15 x9b h4b y101 ff2 fs1e fc0 sc0 ls7 ws6c">, onde </div><div class="c x92 y109 w37 h4a"><div class="t m1f x7 h6d y10a ff3 fs2c fc0 sc0 ls7 ws88">b a</div></div><div class="t m1f x75 h6d y10b ff3 fs2c fc0 sc0 ls7">N</div><div class="c x56 y105 w38 h6e"><div class="t m1f x7 h6d y106 ff3 fs2c fc0 sc0 ls7">h</div></div><div class="c x56 y10c w39 h6f"><div class="t m1f x7 h70 y10d ff4 fs2c fc0 sc0 ls7">−</div></div><div class="t m1f x2e h70 y10b ff4 fs2c fc0 sc0 ls7">=</div><div class="t m15 x8d h4b y101 ff2 fs1e fc0 sc0 ls7 ws6c">. </div><div class="t m15 x3 h4b y10e ff2 fs1e fc0 sc0 ls7 ws6c"> </div><div class="t m1 x15 h3 y10e ff1 fs1 fc0 sc0 ls7 ws6c">Erro da regra </div><div class="c x2d y10f w3a h4a"><div class="t m1f x7 h71 y110 ff2 fs2c fc0 sc0 ls7">1</div></div><div class="c x2d y111 w3b h6e"><div class="t m1f x7 h71 y112 ff2 fs2c fc0 sc0 ls7">3</div></div><div class="t m1 x31 h3 y10e ff1 fs1 fc0 sc0 ls7 ws6c">de Simpson. - </div><div class="t m3 x9c h69 y113 ff2 fs2b fc0 sc0 ls7">5</div><div class="t m3 x9d h69 y114 ff2 fs2b fc0 sc0 ls7 ws89">( 4 )</div><div class="c x9e y115 w3c h5"><div class="t m3 x7 h71 y116 ff2 fs2c fc0 sc0 ls7 ws8a">(<span class="blank _3d"> </span>)<span class="blank _a"> </span>max<span class="blank _c"> </span>( )</div></div><div class="c x99 y111 w35 h4a"><div class="t m3 x7 h71 y112 ff2 fs2c fc0 sc0 ls7 ws8b">90</div></div><div class="t m3 x91 h6a y117 ff3 fs2b fc0 sc0 ls7 ws8c">a t<span class="blank _6b"> </span>b</div><div class="t m3 x1d h6d y118 ff3 fs2c fc0 sc0 ls7 ws8d">Nh</div><div class="c x52 y115 w3d h5"><div class="t m3 x7 h6d y116 ff3 fs2c fc0 sc0 ls7 ws8e">R f<span class="blank _7f"> </span>f<span class="blank _46"> </span>t</div></div><div class="t m3 x81 h6b y117 ff4 fs2b fc0 sc0 ls7 ws87">< <</div><div class="t m3 x10 h70 y10e ff4 fs2c fc0 sc0 ls8">≤<span class="ff2 ls7 ws6c">, onde </span></div><div class="c x9f y111 w3e h6e"><div class="t m3 x7 h71 y112 ff2 fs2c fc0 sc0 ls7">2</div></div><div class="c xa0 y10f w37 h4a"><div class="t m3 x7 h6d y110 ff3 fs2c fc0 sc0 ls7 ws88">b a</div></div><div class="t m3 x55 h6d y119 ff3 fs2c fc0 sc0 ls7">N</div><div class="c xa1 y111 w3f h6e"><div class="t m3 x7 h6d y112 ff3 fs2c fc0 sc0 ls7">h</div></div><div class="c xa2 y11a w39 h6f"><div class="t m3 x7 h70 y11b ff4 fs2c fc0 sc0 ls7">−</div></div><div class="t m3 x32 h70 y119 ff4 fs2c fc0 sc0 ls9">=<span class="ff2 ls7 ws6c v0">. </span></div><div class="t m1 x15 h3 y11c ff1 fs1 fc0 sc0 ls7 ws6c">Erro <span class="blank _6b"> </span>na <span class="blank _6b"> </span>regra </div><div class="c xd y11d w3b h4a"><div class="t m1f x7 h71 y11e ff2 fs2c fc0 sc0 ls7">3</div></div><div class="c xd y11f w3a h6e"><div class="t m1f x7 h71 y120 ff2 fs2c fc0 sc0 ls7">8</div></div><div class="t m1 x62 h3 y11c ff1 fs1 fc0 sc0 ls7 ws6c">de <span class="blank _6b"> </span>Simpson <span class="blank _6b"> </span>- </div><div class="t m20 x73 h72 y121 ff4 fs2d fc0 sc0 ls7 ws8f">( )<span class="blank _80"> </span>( )</div><div class="t m18 x9d h73 y122 ff2 fs2e fc0 sc0 ls7 ws90">5<span class="blank _1b"> </span>( 4 )<span class="blank _81"> </span>4<span class="blank _1b"> </span>( 4 )</div><div class="t m1c x1e h66 y123 ff2 fs29 fc0 sc0 ls7 ws91">3<span class="blank _81"> </span>( )</div><div class="t m1c x90 h66 y124 ff2 fs29 fc0 sc0 ls7 ws92">( )</div><div class="c xa3 y11f w40 h67"><div class="t m1c x7 h66 y125 ff2 fs29 fc0 sc0 ls7 ws93">80 80</div></div><div class="t m1c x71 h74 y123 ff3 fs29 fc0 sc0 ls7 ws94">N<span class="blank _82"> </span>b a</div><div class="t m1c xa4 h74 y124 ff3 fs29 fc0 sc0 ls7 ws95">R<span class="blank _83"> </span>f<span class="blank _84"> </span>h f<span class="blank _85"> </span>h f</div><div class="c x74 y126 w41 h75"><div class="t m21 x7 h76 y127 ff4 fs2f fc0 sc0 ls7 ws96">ξ ξ</div></div><div class="c x78 y128 w42 h77"><div class="t m1c x7 h78 y129 ff4 fs29 fc0 sc0 ls7">−</div></div><div class="t m1c x9a h78 y124 ff4 fs29 fc0 sc0 ls7 ws97">= −<span class="blank _86"> </span>=<span class="blank _48"> </span>−</div><div class="t m1f xa5 h71 y11c ff2 fs2c fc0 sc0 ls7 ws6c"> <span class="blank _6b"> </span>onde </div><div class="c xa6 y12a w3e h6e"><div class="t m1f x7 h71 y12b ff2 fs2c fc0 sc0 ls7">3</div></div><div class="c x42 y12c w37 h4a"><div class="t m1f x7 h6d y12d ff3 fs2c fc0 sc0 ls7 ws98">b a</div></div><div class="t m1f x47 h6d y12e ff3 fs2c fc0 sc0 ls7">N</div><div class="c x15 y12a w43 h6e"><div class="t m1f x7 h6d y12b ff3 fs2c fc0 sc0 ls7">h</div></div><div class="c x63 y12f w39 h6f"><div class="t m1f x7 h70 y130 ff4 fs2c fc0 sc0 ls7">−</div></div><div class="t m1f x64 h70 y12e ff4 fs2c fc0 sc0 ls9">=<span class="ff2 ls7 ws6c v0">e </span></div><div class="c xa7 y131 w44 h3e"><div class="t m1f x7 h69 y132 ff2 fs2b fc0 sc0 ls7 ws99">0 3</div></div><div class="c x2d y131 w45 h8"><div class="t m1f x7 h6a y132 ff3 fs2b fc0 sc0 ls7">N</div></div><div class="c xa8 y133 w46 h5"><div class="t m1f x7 h6d y134 ff3 fs2c fc0 sc0 ls7 ws9a">x x</div></div><div class="t m22 x1 h79 y135 ff4 fs30 fc0 sc0 ls7">ξ</div><div class="t m1f xb h70 y135 ff4 fs2c fc0 sc0 ls7 ws9b">< <<span class="blank _29"> </span><span class="ff2 ws6c">. </span></div><div class="t m9 x3 h7a y136 ff6 fs31 fc0 sc0 ls7 ws6c"> </div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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