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CONSTANTE FUNÇÃO CONSTANTE OU POLINÔMIO DO GRAU ZERO Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 f(x) = k Preencha com números reais as células em branco. 1) Digite um número real para k: f(x) = -3 0 2) Digite números reais para x: x f(x) R 7 -3 0 Correto! -2 -3 0 Correto! 9 -3 0 Correto! 0 -3 0 Correto! -2 -3 0 Correto! 9 -3 0 Correto! OBSERVAÇÕES: Para D(f) = R e k<0 devemos ter f representada por uma reta horizontal abaixo do eixo das abscissas. Para traçar outra reta, atribua novo valor a k. Os valores de x podem ser alterados. CONSTANTE f(x) f(x) PRIMEIRO GRAU FUNÇÃO AFIM OU POLINÔMIO DO PRIMEIRO GRAU Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 f(x) = ax+b Digite um número real não nulo para a e um real para b: (Até dois dígitos para boa visualização) a = 2 b= -6 Valores aceitos. f(x) = 2 x -6 Preencha corretamente as células em branco. x f(x) -6 -18 Correto! 1) O ponto de interseção da reta com o eixo vertical -3 -12 Correto! tem ordenada igual a -4 Tente acertar. 0 -6 Correto! 3 0 Correto! 2) Complete com C se a função é crescente, ou com D, 6 6 Correto! se é decrescente: c Correto pois a>0. 9 12 Correto! 12 18 Correto! 3) Complete com desigualdade (< ou >) na primeira célula à direita de x e o valor correto na seguinte. Se f(x)<0 então x < 2 Tente acertar. Se f(x)>0 então x > 2 Tente acertar. Dx = 3.0 n x f(x) R -3 -6 -18 0 -2 -3 -12 0 -1 0 -6 0 0 3 0 0 1 6 6 0 2 9 12 0 3 12 18 0 PRIMEIRO GRAU f(x) R SEGUNDO GRAU FUNÇÃO QUADRÁTICA OU Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 POLINÔMIO DO SEGUNDO GRAU f(x) = ax2 + bx + c f(x) = 1 x2 0 -6 x + 5 Digite um número real não nulo para a e números reais para b e c: (Até dois dígitos para boa visualização) a = 1 b = -6 c = 5 Valores aceitos. Calcule: D = 16 Correto. Determine as coordenadas do vértice da parábola: ( 3 -4 ) Correto. Determine as raízes reais se existirem: x' = 1 x'' = 5 Raízes corretas. Complete com '<=' ou '>=' e, na célula ao lado, o valor da abscissa conveniente: Para f(x) decrescente deve-se ter x <= 3 Correto. Para f(x) crescente deve-se ter x >= 3 Correto. x inicial = 1 Dx = 2 x f 1.0 0.0 2.0 -3.0 3.0 -4.0 4.0 -3.0 5.0 0.0 6.0 5.0 7.0 12.0 8.0 21.0 9.0 32.0 SEGUNDO GRAU f SEG GRAU FUNÇÃO QUADRÁTICA OU Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 POLINÔMIO DO SEGUNDO GRAU f(x) = ax2 + bx + c f(x) = 1 x2 0 -6 x + 8 O esboço apresentará 17 pontos explícitos, com Dx constante. Digite um número real não nulo para a e números reais para b e c: (Até dois dígitos para boa visualização) a = 1 b = -6 c = 8 Valores aceitos. Calcule: D = 4 Correto. Determine as coordenadas do vértice da parábola: ( 3 -1 ) Correto. Determine as raízes reais se existirem: x' = 2 x'' = 4 Raízes corretas. Considere D(f)=R. Complete com '<=' ou '>=' e, na célula ao lado, o valor da abscissa conveniente: Para f(x) decrescente deve-se ter x <= 3 Correto. Para f(x) crescente deve-se ter x >= 3 Correto. x inicial = -1 Dx = 0.5 x f 0 -1.0 15.0 1 -0.5 11.3 2 0.0 8.0 3 0.5 5.3 4 1.0 3.0 5 1.5 1.3 6 2.0 0.0 7 2.5 -0.8 8 3.0 -1.0 9 3.5 -0.8 10 4.0 0.0 11 4.5 1.3 12 5.0 3.0 13 5.5 5.3 14 6.0 8.0 15 6.5 11.3 16 7.0 15.0 SEG GRAU f EXPONENCIAL FUNÇÃO EXPONENCIAL Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 Dx x (gr) f(x) =K + Q a(Bx+P) assínt f(x) =K + Q aBx+P 0 f(x) = - 4 + 2 x + 3 0.00 0.00 -3.00 -3 -4.00 1.00 1.00 -2.00 -2 -4.00 Dê valor aos parâmetros: 2.00 2.00 -1.00 0 -4.00 (B e Q não nulos, a>0 e a<>1) 3.00 3.00 0.00 4 -4.00 K -4 Válido 4.00 4.00 1.00 12 -4.00 Q 1 Válido 5.00 5.00 2.00 28 -4.00 a 2 Válido 6.00 6.00 3.00 60 -4.00 B 1 Válido 7.00 7.00 4.00 124 -4.00 P 3 Válido 8.00 8.00 4.00 124 -4.00 9.00 9.00 4.00 124 -4.00 xinicial -3 Válido 10.00 10.00 4.00 124 -4.00 Dx 1 Válido 11.00 11.00 4.00 124 -4.00 12.00 12.00 4.00 124 -4.00 Dê valor a xfinal de 13.00 13.00 4.00 124 -4.00 xinicial + 4Dx a xinicial + 30Dx 14.00 14.00 4.00 124 -4.00 15.00 15.00 4.00 124 -4.00 xfinal 4 Válido 16.00 16.00 4.00 124 -4.00 17.00 17.00 4.00 124 -4.00 Parâmetros aceitos. 18.00 18.00 4.00 124 -4.00 19.00 19.00 4.00 124 -4.00 Responda ao que é pedido. 20.00 20.00 4.00 124 -4.00 21.00 21.00 4.00 124 -4.00 1) Equação da assíntota horizontal: 22.00 22.00 4.00 124 -4.00 Y = -4 Correto 0 23.00 23.00 4.00 124 -4.00 24.00 24.00 4.00 124 -4.00 2) Complete com C se a função é crescente, ou com D, se é decrescente: 25.00 25.00 4.00 124 -4.00 c Correto 26.00 26.00 4.00 124 -4.00 27.00 27.00 4.00 124 -4.00 3) Se a função tem raiz, dê o seu valor. 28.00 28.00 4.00 124 -4.00 Se não tem, indique N no espaço em branco. 29.00 29.00 4.00 124 -4.00 x = -1 Correto 30.00 30.00 4.00 124 -4.00 -1 EXPONENCIAL f(x) =K + Q a(Bx+P) assínt LOGARÍTMICA FUNÇÃO LOGARÍTMICA Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 Dx x0assínt x1 f(x) =K + Q a(Bx+P) f(x) =K +Q. loga (Bx+P) Y = 0 + 1 0 log 2 ( 1 x 0 ) 0.00 0.00 0.00 0.06 -4 1.00 0.13 0.00 0.19 -2.4150374993 O esboço apresentará 31 pontos 2.00 0.25 0.00 0.31 -1.6780719051 explícitos, com Dx constante. 3.00 0.38 0.00 0.44 -1.1926450779 4.00 0.50 0.00 0.56 -0.8300749986 Dê valor aos parâmetros: 5.00 0.63 0.00 0.69 -0.5405683814 (B e Q não nulos, a>0 e a<>1) 6.00 0.75 0.00 0.81 -0.2995602819 K 0 Válido 7.00 0.88 0.00 0.94 -0.0931094044 Q 1 Válido 8.00 1.00 0.00 1.06 0.0874628413 a 2 Válido 9.00 1.13 0.00 1.19 0.2479275134 B 1 Válido 10.00 1.25 0.00 1.31 0.3923174228 P 0 Válido 11.00 1.38 0.00 1.44 0.5235619561 12.00 1.50 0.00 1.56 0.6438561898 x inicial 0.0625 Válido 13.00 1.63 0.00 1.69 0.7548875022 Dx 0.125 Válido 14.00 1.75 0.00 1.81 0.8579809951 15.00 1.88 0.00 1.94 0.9541963104 Parâmetros aceitos. 16.00 2.00 0.00 2.06 1.0443941194 17.00 2.13 0.00 2.19 1.1292830169 Responda ao que é pedido. 18.00 2.25 0.00 2.31 1.2094533656 19.00 2.38 0.00 2.44 1.2854022189 1) Equação da assíntota vertical: 0 20.00 2.50 0.00 2.56 1.3575520046 21.00 2.63 0.00 2.69 1.4262647547 x = 0 Correto 22.00 2.75 0.00 2.81 1.4918530963 0 23.00 2.88 0.00 2.94 1.5545888517 3) Dê o valor da raiz da função. 24.00 3.00 0.00 3.06 1.6147098441 25.00 3.13 0.00 3.19 1.672425342 x = 1 Correto 26.00 3.25 0.00 3.31 1.7279204546 27.00 3.38 0.00 3.44 1.7813597135 2) Complete com C se a função é crescente, ou com D, se é decrescente: 28.00 3.50 0.00 3.56 1.8328900142 29.00 3.63 0.00 3.69 1.8826430494 c Correto 30.00 3.75 0.00 3.81 1.9307373376 1 LOGARÍTMICA SENO FUNÇÕES SENOIDAIS Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 DX = 0.94 x (gr) y=A+Bsen(Kx+P) f(x) = A + B sen(Kx+P) Y = 0 + 1 sen( 1 x 0 ) 0 -180.0 -0.00 1 -179.1 -0.02 Use valor de 2 -178.1 -0.03 ângulo em graus. 3 -177.2 -0.05 4 -176.3 -0.07 5 -175.3 -0.08 Dê valor aos parâmetros: 6 -174.4 -0.10 7 -173.4 -0.11 A 0 8 -172.5 -0.13 B 1 9 -171.6 -0.15 K 1 10 -170.6 -0.16 P 0 11 -169.7 -0.18 x inicial -180 12 -168.8 -0.20 períodos 2 13 -167.8 -0.21 Valores aceitos. 14 -166.9 -0.23 15 -165.9 -0.24 16 -165.0 -0.26 Responda ao que é pedido, considerando D(f) = R: 17 -164.1 -0.27 18 -163.1 -0.29 Período da função = 360 Correto. 19 -162.2 -0.31 20 -161.3 -0.32 Amplitude da onda = 1 Correto. 21 -160.3 -0.34 22 -159.4 -0.35 Elementos imagem = -1 a 1 Correto. 23 -158.4 -0.37 24 -157.5 -0.38 25 -156.6 -0.40 26 -155.6 -0.41 27 -154.7 -0.43 28 -153.8 -0.44 29 -152.8 -0.46 30 -151.9 -0.47 31 -150.9 -0.49 32 -150.0 -0.50 33 -149.1 -0.51 34 -148.1 -0.53 35 -147.2 -0.54 36 -146.3 -0.56 37 -145.3 -0.57 38 -144.4 -0.58 39 -143.4 -0.60 40 -142.5 -0.61 41 -141.6 -0.62 42 -140.6 -0.63 43 -139.7 -0.65 44 -138.8 -0.66 45 -137.8 -0.67 46 -136.9 -0.68 47 -135.9 -0.70 48 -135.0 -0.71 49 -134.1 -0.72 50 -133.1 -0.73 51 -132.2 -0.74 52 -131.3 -0.75 53 -130.3 -0.76 54 -129.4 -0.77 55 -128.4 -0.78 56 -127.5 -0.79 57 -126.6 -0.80 58 -125.6 -0.81 59 -124.7 -0.82 60 -123.8 -0.83 61 -122.8 -0.84 62 -121.9 -0.85 63 -120.9 -0.86 64 -120.0 -0.87 65 -119.1 -0.87 66 -118.1 -0.88 67 -117.2 -0.89 68 -116.3 -0.90 69 -115.3 -0.90 70 -114.4 -0.91 71 -113.4 -0.92 72 -112.5 -0.92 73 -111.6 -0.93 74 -110.6 -0.94 75 -109.7 -0.94 76 -108.8 -0.95 77 -107.8 -0.95 78 -106.9 -0.96 79 -105.9 -0.96 80 -105.0 -0.97 81 -104.1 -0.97 82 -103.1 -0.97 83 -102.2 -0.98 84 -101.3 -0.98 85 -100.3 -0.98 86 -99.4 -0.99 87 -98.4 -0.99 88 -97.5 -0.99 89 -96.6 -0.99 90 -95.6 -1.00 91 -94.7 -1.00 92 -93.8 -1.00 93 -92.8 -1.00 94 -91.9 -1.00 95 -90.9 -1.00 96 -90.0 -1.00 97 -89.1 -1.00 98 -88.1 -1.00 99 -87.2 -1.00 100 -86.3 -1.00 101 -85.3 -1.00 102 -84.4 -1.00 103 -83.4 -0.99 104 -82.5 -0.99 105 -81.6 -0.99 106 -80.6 -0.99 107 -79.7 -0.98 108 -78.8 -0.98 109 -77.8 -0.98 110 -76.9 -0.97 111 -75.9 -0.97 112 -75.0 -0.97 113 -74.1 -0.96 114 -73.1 -0.96 115 -72.2 -0.95 116 -71.3 -0.95 117 -70.3 -0.94 118 -69.4 -0.94 119 -68.4 -0.93 120 -67.5 -0.92 121 -66.6 -0.92 122 -65.6 -0.91 123 -64.7 -0.90 124 -63.8 -0.90 125 -62.8 -0.89 126 -61.9 -0.88 127 -60.9 -0.87 128 -60.0 -0.87 129 -59.1 -0.86 130 -58.1 -0.85 131 -57.2 -0.84 132 -56.3 -0.83 133 -55.3 -0.82 134 -54.4 -0.81 135 -53.4 -0.80 136 -52.5 -0.79 137 -51.6 -0.78 138 -50.6 -0.77 139 -49.7 -0.76 140 -48.8 -0.75 141 -47.8 -0.74 142 -46.9 -0.73 143 -45.9 -0.72 144 -45.0 -0.71 145 -44.1 -0.70 146 -43.1 -0.68 147 -42.2 -0.67 148 -41.3 -0.66 149 -40.3 -0.65 150 -39.4 -0.63 151 -38.4 -0.62 152 -37.5 -0.61 153 -36.6 -0.60 154 -35.6 -0.58 155 -34.7 -0.57 156 -33.8 -0.56 157 -32.8 -0.54 158 -31.9 -0.53 159 -30.9 -0.51 160 -30.0 -0.50 161 -29.1 -0.49 162 -28.1 -0.47 163 -27.2 -0.46 164 -26.3 -0.44 165 -25.3 -0.43 166 -24.4 -0.41 167 -23.4 -0.40 168 -22.5 -0.38 169 -21.6 -0.37 170 -20.6 -0.35 171 -19.7 -0.34 172 -18.8 -0.32 173 -17.8 -0.31 174 -16.9 -0.29 175 -15.9 -0.27 176 -15.0 -0.26 177 -14.1 -0.24 178 -13.1 -0.23 179 -12.2 -0.21 180 -11.3 -0.20 181 -10.3 -0.18 182 -9.4 -0.16 183 -8.4 -0.15 184 -7.5 -0.13 185 -6.6 -0.11 186 -5.6 -0.10 187 -4.7 -0.08 188 -3.8 -0.07 189 -2.8 -0.05 190 -1.9 -0.03 191 -0.9 -0.02 192 0.0 0.00 193 0.9 0.02 194 1.9 0.03 195 2.8 0.05 196 3.8 0.07 197 4.7 0.08 198 5.6 0.10 199 6.6 0.11 200 7.5 0.13 201 8.4 0.15 202 9.4 0.16 203 10.3 0.18 204 11.3 0.20 205 12.2 0.21 206 13.1 0.23 207 14.1 0.24 208 15.0 0.26 209 15.9 0.27 210 16.9 0.29 211 17.8 0.31 212 18.8 0.32 213 19.7 0.34 214 20.6 0.35 215 21.6 0.37 216 22.5 0.38 217 23.4 0.40 218 24.4 0.41 219 25.3 0.43 220 26.3 0.44 221 27.2 0.46 222 28.1 0.47 223 29.1 0.49 224 30.0 0.50 225 30.9 0.51 226 31.9 0.53 227 32.8 0.54 228 33.8 0.56 229 34.7 0.57 230 35.6 0.58 231 36.6 0.60 232 37.5 0.61 233 38.4 0.62 234 39.4 0.63 235 40.3 0.65 236 41.3 0.66 237 42.2 0.67 238 43.1 0.68 239 44.1 0.70 240 45.0 0.71 241 45.9 0.72 242 46.9 0.73 243 47.8 0.74 244 48.8 0.75 245 49.7 0.76 246 50.6 0.77 247 51.6 0.78 248 52.5 0.79 249 53.4 0.80 250 54.4 0.81 251 55.3 0.82 252 56.3 0.83 253 57.2 0.84 254 58.1 0.85 255 59.1 0.86 256 60.0 0.87 257 60.9 0.87 258 61.9 0.88 259 62.8 0.89 260 63.8 0.90 261 64.7 0.90 262 65.6 0.91 263 66.6 0.92 264 67.5 0.92 265 68.4 0.93 266 69.4 0.94 267 70.3 0.94 268 71.3 0.95 269 72.2 0.95 270 73.1 0.96 271 74.1 0.96 272 75.0 0.97 273 75.9 0.97 274 76.9 0.97 275 77.8 0.98 276 78.8 0.98 277 79.7 0.98 278 80.6 0.99 279 81.6 0.99 280 82.5 0.99 281 83.4 0.99 282 84.4 1.00 283 85.3 1.00 284 86.3 1.00 285 87.2 1.00 286 88.1 1.00 287 89.1 1.00 288 90.0 1.00 289 90.9 1.00 290 91.9 1.00 291 92.8 1.00 292 93.8 1.00 293 94.7 1.00 294 95.6 1.00 295 96.6 0.99 296 97.5 0.99 297 98.4 0.99 298 99.4 0.99 299 100.3 0.98 300 101.3 0.98 301 102.2 0.98 302 103.1 0.97 303 104.1 0.97 304 105.0 0.97 305 105.9 0.96 306 106.9 0.96 307 107.8 0.95 308 108.8 0.95 309 109.7 0.94 310 110.6 0.94 311 111.6 0.93 312 112.5 0.92 313 113.4 0.92 314 114.4 0.91 315 115.3 0.90 316 116.3 0.90 317 117.2 0.89 318 118.1 0.88 319 119.1 0.87 320 120.0 0.87 321 120.9 0.86 322 121.9 0.85 323 122.8 0.84 324 123.8 0.83 325 124.7 0.82 326 125.6 0.81 327 126.6 0.80 328 127.5 0.79 329 128.4 0.78 330 129.4 0.77 331 130.3 0.76 332 131.3 0.75 333 132.2 0.74 334 133.1 0.73 335 134.1 0.72 336 135.0 0.71 337 135.9 0.70 338 136.9 0.68 339 137.8 0.67 340 138.8 0.66 341 139.7 0.65 342 140.6 0.63 343 141.6 0.62 344 142.5 0.61 345 143.4 0.60 346 144.4 0.58 347 145.3 0.57 348 146.3 0.56 349 147.2 0.54 350 148.1 0.53 351 149.1 0.51 352 150.0 0.50 353 150.9 0.49 354 151.9 0.47 355 152.8 0.46 356 153.8 0.44 357 154.7 0.43 358 155.6 0.41 359 156.6 0.40 360 157.5 0.38 361 158.4 0.37 362 159.4 0.35 363 160.3 0.34 364 161.3 0.32 365 162.2 0.31 366 163.1 0.29 367 164.1 0.27 368 165.0 0.26 369 165.9 0.24 370 166.9 0.23 371 167.8 0.21 372 168.8 0.20 373 169.7 0.18 374 170.6 0.16 375 171.6 0.15 376 172.5 0.13 377 173.4 0.11 378 174.4 0.10 379 175.3 0.08 380 176.3 0.07 381 177.2 0.05 382 178.1 0.03 383 179.1 0.02 384 180.0 0.00 385 180.9 -0.02 386 181.9 -0.03 387 182.8 -0.05 388 183.8 -0.07 389 184.7 -0.08 390 185.6 -0.10 391 186.6 -0.11 392 187.5 -0.13 393 188.4 -0.15 394 189.4 -0.16 395 190.3 -0.18 396 191.3 -0.20 397 192.2 -0.21 398 193.1 -0.23 399 194.1 -0.24 400 195.0 -0.26 401 195.9 -0.27 402 196.9 -0.29 403 197.8 -0.31 404 198.8 -0.32 405 199.7 -0.34 406 200.6 -0.35 407 201.6 -0.37 408 202.5 -0.38 409 203.4 -0.40 410 204.4 -0.41 411 205.3 -0.43 412 206.3 -0.44 413 207.2 -0.46 414 208.1 -0.47 415 209.1 -0.49 416 210.0 -0.50 417 210.9 -0.51 418 211.9 -0.53 419 212.8 -0.54 420 213.8 -0.56 421 214.7 -0.57 422 215.6 -0.58 423 216.6 -0.60 424 217.5 -0.61 425 218.4 -0.62 426 219.4 -0.63 427 220.3 -0.65 428 221.3 -0.66 429 222.2 -0.67 430 223.1 -0.68 431 224.1 -0.70 432 225.0 -0.71 433 225.9 -0.72 434 226.9 -0.73 435 227.8 -0.74 436 228.8 -0.75 437 229.7 -0.76 438 230.6 -0.77 439 231.6 -0.78 440 232.5 -0.79 441 233.4 -0.80 442 234.4 -0.81 443 235.3 -0.82 444 236.3 -0.83 445 237.2 -0.84 446 238.1 -0.85 447 239.1 -0.86 448 240.0 -0.87 449 240.9 -0.87 450 241.9 -0.88 451 242.8 -0.89 452 243.8 -0.90 453 244.7 -0.90 454 245.6 -0.91 455 246.6 -0.92 456 247.5 -0.92 457 248.4 -0.93 458 249.4 -0.94 459 250.3 -0.94 460 251.3 -0.95 461 252.2 -0.95 462 253.1 -0.96 463 254.1 -0.96 464 255.0 -0.97 465 255.9 -0.97 466 256.9 -0.97 467 257.8 -0.98 468 258.8 -0.98 469 259.7 -0.98 470 260.6 -0.99 471 261.6 -0.99 472 262.5 -0.99 473 263.4 -0.99 474 264.4 -1.00 475 265.3 -1.00 476 266.3 -1.00 477 267.2 -1.00 478 268.1 -1.00 479 269.1 -1.00 480 270.0 -1.00 481 270.9 -1.00 482 271.9 -1.00 483 272.8 -1.00 484 273.8 -1.00 485 274.7 -1.00 486 275.6 -1.00 487 276.6 -0.99 488 277.5 -0.99 489 278.4 -0.99 490 279.4 -0.99 491 280.3 -0.98 492 281.3 -0.98 493 282.2 -0.98 494 283.1 -0.97 495 284.1 -0.97 496 285.0 -0.97 497 285.9 -0.96 498 286.9 -0.96 499 287.8 -0.95 500 288.8 -0.95 501 289.7 -0.94 502 290.6 -0.94 503 291.6 -0.93 504 292.5 -0.92 505 293.4 -0.92 506 294.4 -0.91 507 295.3 -0.90 508 296.3 -0.90 509 297.2 -0.89 510 298.1 -0.88 511 299.1 -0.87 512 300.0 -0.87 513 300.9 -0.86 514 301.9 -0.85 515 302.8 -0.84 516 303.8 -0.83 517 304.7 -0.82 518 305.6 -0.81 519 306.6 -0.80 520 307.5 -0.79 521 308.4 -0.78 522 309.4 -0.77 523 310.3 -0.76 524 311.3 -0.75 525 312.2 -0.74 526 313.1 -0.73 527 314.1 -0.72 528 315.0 -0.71 529 315.9 -0.70 530 316.9 -0.68 531 317.8 -0.67 532 318.8 -0.66 533 319.7 -0.65 534 320.6 -0.63 535 321.6 -0.62 536 322.5 -0.61 537 323.4 -0.60 538 324.4 -0.58 539 325.3 -0.57 540 326.3 -0.56 541 327.2 -0.54 542 328.1 -0.53 543 329.1 -0.51 544 330.0 -0.50 545 330.9 -0.49 546 331.9 -0.47 547 332.8 -0.46 548 333.8 -0.44 549 334.7 -0.43 550 335.6 -0.41 551 336.6 -0.40 552 337.5 -0.38 553 338.4 -0.37 554 339.4 -0.35 555 340.3 -0.34 556 341.3 -0.32 557 342.2 -0.31 558 343.1 -0.29 559 344.1 -0.27 560 345.0 -0.26 561 345.9 -0.24 562 346.9 -0.23 563 347.8 -0.21 564 348.8 -0.20 565 349.7 -0.18 566 350.6 -0.16 567 351.6 -0.15 568 352.5 -0.13 569 353.4 -0.11 570 354.4 -0.10 571 355.3 -0.08 572 356.3 -0.07 573 357.2 -0.05 574 358.1 -0.03 575 359.1 -0.02 576 360.0 -0.00 577 360.9 0.02 578 361.9 0.03 579 362.8 0.05 580 363.8 0.07 581 364.7 0.08 582 365.6 0.10 583 366.6 0.11 584 367.5 0.13 585 368.4 0.15 586 369.4 0.16 587 370.3 0.18 588 371.3 0.20 589 372.2 0.21 590 373.1 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724 498.8 0.66 725 499.7 0.65 726 500.6 0.63 727 501.6 0.62 728 502.5 0.61 729 503.4 0.60 730 504.4 0.58 731 505.3 0.57 732 506.3 0.56 733 507.2 0.54 734 508.1 0.53 735 509.1 0.51 736 510.0 0.50 737 510.9 0.49 738 511.9 0.47 739 512.8 0.46 740 513.8 0.44 741 514.7 0.43 742 515.6 0.41 743 516.6 0.40 744 517.5 0.38 745 518.4 0.37 746 519.4 0.35 747 520.3 0.34 748 521.3 0.32 749 522.2 0.31 750 523.1 0.29 751 524.1 0.27 752 525.0 0.26 753 525.9 0.24 754 526.9 0.23 755 527.8 0.21 756 528.8 0.20 757 529.7 0.18 758 530.6 0.16 759 531.6 0.15 760 532.5 0.13 761 533.4 0.11 762 534.4 0.10 763 535.3 0.08 764 536.3 0.07 765 537.2 0.05 766 538.1 0.03 767 539.1 0.02 768 540.0 0.00 SENO y=A+Bsen(Kx+P) COSSENO FUNÇÕES COSSENOIDAIS Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 DX = 0.94 x (gr) y=A+Bcos(Kx+P) f(x) = A + B cos(Kx+P) Y = 0 + 1 cos( 2 x 0 ) 0 -720.0 1.00 1 -719.1 1.00 Use valor de 2 -718.1 1.00 ângulo em graus. 3 -717.2 1.00 4 -716.3 0.99 5 -715.3 0.99 Dê valor aos parâmetros: 6 -714.4 0.98 7 -713.4 0.97 A 0 8 -712.5 0.97 B 1 9 -711.6 0.96 K 2 10 -710.6 0.95 P 0 11 -709.7 0.94 x inicial -720 12 -708.8 0.92 períodos 4 13 -707.8 0.91 Valores aceitos. 14 -706.9 0.90 15 -705.9 0.88 16 -705.0 0.87 Responda ao que é pedido, considerando D(f) = R: 17 -704.1 0.85 18 -703.1 0.83 Período da função = 180 Correto. 19 -702.2 0.81 20 -701.3 0.79 Amplitude da onda = 1 Correto. 21 -700.3 0.77 22 -699.4 0.75 Elementos imagem = -1 a 1 Correto. 23 -698.4 0.73 24 -697.5 0.71 25 -696.6 0.68 26 -695.6 0.66 27 -694.7 0.63 28 -693.8 0.61 29 -692.8 0.58 30 -691.9 0.56 31 -690.9 0.53 32 -690.0 0.50 33 -689.1 0.47 34 -688.1 0.44 35 -687.2 0.41 36 -686.3 0.38 37 -685.3 0.35 38 -684.4 0.32 39 -683.4 0.29 40 -682.5 0.26 41 -681.6 0.23 42 -680.6 0.20 43 -679.7 0.16 44 -678.8 0.13 45 -677.8 0.10 46 -676.9 0.07 47 -675.9 0.03 48 -675.0 0.00 49 -674.1 -0.03 50 -673.1 -0.07 51 -672.2 -0.10 52 -671.3 -0.13 53 -670.3 -0.16 54 -669.4 -0.20 55 -668.4 -0.23 56 -667.5 -0.26 57 -666.6 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0.61 605 -152.8 0.58 606 -151.9 0.56 607 -150.9 0.53 608 -150.0 0.50 609 -149.1 0.47 610 -148.1 0.44 611 -147.2 0.41 612 -146.3 0.38 613 -145.3 0.35 614 -144.4 0.32 615 -143.4 0.29 616 -142.5 0.26 617 -141.6 0.23 618 -140.6 0.20 619 -139.7 0.16 620 -138.8 0.13 621 -137.8 0.10 622 -136.9 0.07 623 -135.9 0.03 624 -135.0 -0.00 625 -134.1 -0.03 626 -133.1 -0.07 627 -132.2 -0.10 628 -131.3 -0.13 629 -130.3 -0.16 630 -129.4 -0.20 631 -128.4 -0.23 632 -127.5 -0.26 633 -126.6 -0.29 634 -125.6 -0.32 635 -124.7 -0.35 636 -123.8 -0.38 637 -122.8 -0.41 638 -121.9 -0.44 639 -120.9 -0.47 640 -120.0 -0.50 641 -119.1 -0.53 642 -118.1 -0.56 643 -117.2 -0.58 644 -116.3 -0.61 645 -115.3 -0.63 646 -114.4 -0.66 647 -113.4 -0.68 648 -112.5 -0.71 649 -111.6 -0.73 650 -110.6 -0.75 651 -109.7 -0.77 652 -108.8 -0.79 653 -107.8 -0.81 654 -106.9 -0.83 655 -105.9 -0.85 656 -105.0 -0.87 657 -104.1 -0.88 658 -103.1 -0.90 659 -102.2 -0.91 660 -101.3 -0.92 661 -100.3 -0.94 662 -99.4 -0.95 663 -98.4 -0.96 664 -97.5 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0.23 728 -37.5 0.26 729 -36.6 0.29 730 -35.6 0.32 731 -34.7 0.35 732 -33.8 0.38 733 -32.8 0.41 734 -31.9 0.44 735 -30.9 0.47 736 -30.0 0.50 737 -29.1 0.53 738 -28.1 0.56 739 -27.2 0.58 740 -26.3 0.61 741 -25.3 0.63 742 -24.4 0.66 743 -23.4 0.68 744 -22.5 0.71 745 -21.6 0.73 746 -20.6 0.75 747 -19.7 0.77 748 -18.8 0.79 749 -17.8 0.81 750 -16.9 0.83 751 -15.9 0.85 752 -15.0 0.87 753 -14.1 0.88 754 -13.1 0.90 755 -12.2 0.91 756 -11.3 0.92 757 -10.3 0.94 758 -9.4 0.95 759 -8.4 0.96 760 -7.5 0.97 761 -6.6 0.97 762 -5.6 0.98 763 -4.7 0.99 764 -3.8 0.99 765 -2.8 1.00 766 -1.9 1.00 767 -0.9 1.00 768 0.0 1.00 COSSENO y=A+Bcos(Kx+P) TANGENTE FUNÇÃO TANGENTE Nízio Geraldo dos Santos - Professor na UNA e FPL - 25/02/2014 Dx 0.31 x (gr) y=A+Btan(Kx+P) assínt mín máx f(x) = A + B tan(Kx+P) Y = 0 + 1 tan( 3 x 0 ) 0 -90.0 0.00 -10.00 -10.00 10.00 1 -89.7 -10.00 0.00 -10.00 10.00 Use valor de 2 -89.4 -10.00 0.00 -10.00 10.00 ângulo em graus. 3 -89.1 -10.00 0.00 -10.00 10.00 4 -88.8 -10.00 0.00 -10.00 10.00 Dê valor aos parâmetros: 5 -88.4 -10.00 0.00 -10.00 10.00 (B e K não nulos) 6 -88.1 -10.00 0.00 -10.00 10.00 A 0 7 -87.8 -8.69 0.00 -10.00 10.00 B 1 8 -87.5 -7.60 0.00 -10.00 10.00 K 3 9 -87.2 -6.74 0.00 -10.00 10.00 P 0 10 -86.9 -6.06 0.00 -10.00 10.00 11 -86.6 -5.50 0.00 -10.00 10.00 x inicial -90 12 -86.3 -5.03 0.00 -10.00 10.00 13 -85.9 -4.63 0.00 -10.00 10.00 períodos 4 14 -85.6 -4.29 0.00 -10.00 10.00 15 -85.3 -3.99 0.00 -10.00 10.00 F. MÍN = -10 16 -85.0 -3.73 0.00 -10.00 10.00 F. MÁX = 10 17 -84.7 -3.50 0.00 -10.00 10.00 Valores aceitos. 19 -84.1 -3.11 0.00 -10.00 10.00 20 -83.8 -2.95 0.00 -10.00 10.00 Responda ao que é pedido. 21 -83.4 -2.79 0.00 -10.00 10.00 22 -83.1 -2.66 0.00 -10.00 10.00 1) Período da função= 180 Incorreto. 23 -82.8 -2.53 0.00 -10.00 10.00 24 -82.5 -2.41 0.00 -10.00 10.00 2) Complete com C se a função é crescente, ou com D, se é decrescente: 25 -82.2 -2.31 0.00 -10.00 10.00 d Incorreto. 26 -81.9 -2.21 0.00 -10.00 10.00 27 -81.6 -2.11 0.00 -10.00 10.00 28 -81.3 -2.03 0.00 -10.00 10.00 29 -80.9 -1.95 0.00 -10.00 10.00 30 -80.6 -1.87 0.00 -10.00 10.00 31 -80.3 -1.80 0.00 -10.00 10.00 32 -80.0 -1.73 0.00 -10.00 10.00 33 -79.7 -1.67 0.00 -10.00 10.00 34 -79.4 -1.61 0.00 -10.00 10.00 35 -79.1 -1.55 0.00 -10.00 10.00 36 -78.8 -1.50 0.00 -10.00 10.00 37 -78.4 -1.44 0.00 -10.00 10.00 38 -78.1 -1.40 0.00 -10.00 10.00 39 -77.8 -1.35 0.00 -10.00 10.00 40 -77.5 -1.30 0.00 -10.00 10.00 41 -77.2 -1.26 0.00 -10.00 10.00 42 -76.9 -1.22 0.00 -10.00 10.00 43 -76.6 -1.18 0.00 -10.00 10.00 44 -76.3 -1.14 0.00 -10.00 10.00 45 -75.9 -1.10 0.00 -10.00 10.00 46 -75.6 -1.07 0.00 -10.00 10.00 47 -75.3 -1.03 0.00 -10.00 10.00 48 -75.0 -1.00 0.00 -10.00 10.00 49 -74.7 -0.97 0.00 -10.00 10.00 50 -74.4 -0.94 0.00 -10.00 10.00 51 -74.1 -0.91 0.00 -10.00 10.00 52 -73.8 -0.88 0.00 -10.00 10.00 53 -73.4 -0.85 0.00 -10.00 10.00 54 -73.1 -0.82 0.00 -10.00 10.00 55 -72.8 -0.79 0.00 -10.00 10.00 56 -72.5 -0.77 0.00 -10.00 10.00 57 -72.2 -0.74 0.00 -10.00 10.00 58 -71.9 -0.72 0.00 -10.00 10.00 59 -71.6 -0.69 0.00 -10.00 10.00 60 -71.3 -0.67 0.00 -10.00 10.00 61 -70.9 -0.64 0.00 -10.00 10.00 62 -70.6 -0.62 0.00 -10.00 10.00 63 -70.3 -0.60 0.00 -10.00 10.00 64 -70.0 -0.58 0.00 -10.00 10.00 65 -69.7 -0.56 0.00 -10.00 10.00 66 -69.4 -0.53 0.00 -10.00 10.00 67 -69.1 -0.51 0.00 -10.00 10.00 68 -68.8 -0.49 0.00 -10.00 10.00 69 -68.4 -0.47 0.00 -10.00 10.00 70 -68.1 -0.45 0.00 -10.00 10.00 71 -67.8 -0.43 0.00 -10.00 10.00 72 -67.5 -0.41 0.00 -10.00 10.00 73 -67.2 -0.40 0.00 -10.00 10.00 74 -66.9 -0.38 0.00 -10.00 10.00 75 -66.6 -0.36 0.00 -10.00 10.00 76 -66.3 -0.34 0.00 -10.00 10.00 77 -65.9 -0.32 0.00 -10.00 10.00 78 -65.6 -0.30 0.00 -10.00 10.00 79 -65.3 -0.29 0.00 -10.00 10.00 80 -65.0 -0.27 0.00 -10.00 10.00 81 -64.7 -0.25 0.00 -10.00 10.00 82 -64.4 -0.23 0.00 -10.00 10.00 83 -64.1 -0.22 0.00 -10.00 10.00 84 -63.8 -0.20 0.00 -10.00 10.00 85 -63.4 -0.18 0.00 -10.00 10.00 86 -63.1 -0.17 0.00 -10.00 10.00 87 -62.8 -0.15 0.00 -10.00 10.00 88 -62.5 -0.13 0.00 -10.00 10.00 89 -62.2 -0.12 0.00 -10.00 10.00 90 -61.9 -0.10 0.00 -10.00 10.00 91 -61.6 -0.08 0.00 -10.00 10.00 92 -61.3 -0.07 0.00 -10.00 10.00 93 -60.9 -0.05 0.00 -10.00 10.00 94 -60.6 -0.03 0.00 -10.00 10.00 95 -60.3 -0.02 0.00 -10.00 10.00 96 -60.0 0.00 0.00 -10.00 10.00 97 -59.7 0.02 0.00 -10.00 10.00
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