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1) Agricultura atual Terra Nossa 20-10-10 10-10-20 100kg 300kg 100+300=400 20+30=50 (50/400)x100=12,5% 10+30=40 (40/400)x100=10% 10+60=70 (70/400)x100=17,5% 12,5-10-17,5 B 2) a=(y2-y1)/(x2-x1) 0=-2.35+b a=(60-0)/(5-35) b-70=0 a=60/-30 b=70 a=-2 y=-2x+70 2x=-y+70 X=-0,5y+35 A 3) h=-4,9t2 + 49 Taxa de variação Altura do prédio = 49cm dh/dt=h′(t)=-9,8t 0=-4,9t2+49 4,9t2=49 t2=10 t2=3,16s Tempo de queda é de aproximadamente 3,2s D 4) IB(t)=t2-24t+143 xv=-b/2a yv=-b2-4ac/4ª xv=-(-24/2) yv=-(576-572/4) xv=12 yv=-4/4 yv=-1 tmin=12 IBmin=-1 E 5) Segmento AB AB=(1-(-2),-4-3) A=(-2,3) AB=(3,-7) B=(1,-4) E 6) cos 0° = 1 v3=1,732 u.v.θ 45°= 0,707 6.9.-0,866 90°= 0 -46,764=-27v3 150°=-0,866 180°=-1 B 7) u+v u=2i+3j-k v=-i+2j u+v=i+5j-k u.v u.v=2.-1i3.2j-1.0k u.v=-2i+6j B 8) u=5i+2j-k v=-4i+2j+k u.v= 5.-4i2.2j-1.1k u.v=-20i+4j-k u.v=-20+4-1 u.v=-17 C 9) V(t)=15t2-750t+9000 V(3)= 15(3)2-750(3)+9000 V(3)=135-2250+9000 V(3)=6885 A 10) ∆v/∆t=v′=2.15t-750 v′=30t-750 v′=30.3-750 v′=90-750 v′=660L/h E 11) v(t)=-4,5t2+18t v′=-9t+18 v(t)=-4,5.(2)2+18.2 9t-18=0 v(t)=-18+36 9t=18 v(t)=18m/s t=2s D 12) │u│= √(-3)2+42+02 -0,6/-3=0,8/4 │u│= √9+16+0 - 0,6.4=-3.0,8 │u│= √25 -2,4=-2,4 │u│= 5 1=√(-0,6)2 + 0,82 9/-3=-12/4 1=√0,36+0,64 4.9=-12.-3 1=√1 36=36 │u│=√92+122 │u│=√81+144 │u│= √225 │u│= 15 A 13) w=α.u+β.v (-17,12)=α.(-2,0)+β.(3,-4) (-17,12)=-2α+3β;-4β+0 -4β=12 -2α+3β=-17 -β=3 -2α+3.-3=-17 β=-3 -2α=-17+9 -2α=-8 α=4 A 14) AO+DE+PL+FQ+IH AO+OD+DM+ML+LP AP A 15) AQ=AC+CG+GQ AQ=AC+AE+2/3GH AQ=AE+AC+2/3AB E 16) u=(1,-2) 2u=(2,-4) V=(-4,0) 4v=(-16,0) 2u-4v=(2-(-16).-4-0) 2u-4v=(18.-4) u=(1,-2) │u+v│=√(-3)2+(-2)2 v=(-3,0) │u+v│=√9+4 u+v=(-3,-2) │u+v│=√13 1/4=-2/0 8≠0 D 17) x+12/6=3/9 9(x+12)=3.6 9x+108=18 9x=-108+18 9x=-90 X=-10 B 18) │s│=√32+(-6)2 │s│=√9+36 │s│=√45 │s│= 3√5 D 19) AB=(x2-x1,y2-y1) A(-1,3) B(0,-4) AB=(0-(-1),-4-3) AB=(1,-7) 1/4=-7/28 1.28=-4.-7 28=28 B 20) AB=(x2-x1,y2-y1) A=(-1,0) B(-2,1) AB=(-2-(-1),1-0) AB=(-1,1) │AB│=√(-1)2+12 AB/│AB│=(-1/√2, 1/√2) │AB│=√1+1 AB/│AB│=(-1.√2/√2.√2,1.√2/√2.√2) │AB│=√2 AB/│AB│=(-√2/2,√2/2) B 21) V(t)=6t3+1,5t V(t)=6.23+1,5.2 V(t)=6.8+3 V(t)=48+3 V(t)=51 C 22) V(t)=6.t3+1,5t V′=3.6t2+1,5 V′=18t2+1,5 V′=18.22+1,5 V′=18.4+1,5 V′=72+1,5 V′=73,5 L/min B 23) y=(x+16).senx y′=u′.v+u.v′ y′=1.senx+(x+16).cosx y′=senx+(x+16).cosx B 24) f(x)=x3-8 xo=-2 y′=3x2 a=f′(-2) f′(-2)=3.(-2)2 f′(-2)=3.4 f′(-2)=12 A 25) f(x)=ex.sen(2x) u=2x f′(x)=(ex.senu+ex.cosu).u′ u=2 f′(x)=((ex.(senu+cosu)).u′ f′(x)=((ex′(sen2x+cos2x)).2 f′(0)=((e0.(sen2.0+cos2.0)).2 f′(0)=((1.(0+1)).2 f′(0)=1.2 f′(0)=2 A 26) u=(2,4) u.v=(2.0+4.-3) v=(0,3) u.v=(0+12) u.v=12 E 27) u=(2,-4) 2.u=(2.2,2-4) 2u(4,-8) v=(1,-2) 5.v=(5.1,5.-2) 5v(5,-10) 2u.5v=(4.5+(-8.-10)) 2u.5v=(20+80) 2u.5v=100 C 28) u=(2,-4,2) A=│u˄v│ v=(1,-4,0) |ij k i j| ijk |u˄v|=|1-40 1-4| -80-4 |2-42 2-4| - (0-28) (-8,-2,4) A=|(-8,-2,4)|=√(-8)²+(-2)²+4²=√84 A=2˄√21 A 29) |u|=2 A=b.h |v|=3 A=|u|.|v|.senθ/2 θ=30º A=2.3.0,5/2 A=1,5uA E 30) u=(1,-2,-1) v=(2,1,0) w.u=0 (a,b,c).(1,-2,-1)=a-2b-c=0 w.v=0 (a,b,c).(2,1,0)=2a+b =0 a-2b-c=0 w=√2²+(-4)²+10²=2√30 2a+b =0 w=√4+16+100=2√30 a²+b²+c²=2√30 w=√120=2√30 w=2√30=2√30 2a+b=0 a-2b-c=0 2.2-4=0 2-(-2.-4)-10=0 w=(2,-4,10) 0=0 2+8-10=0 |w|=2√30 0=0 B 31) u=(1,-2,-1) v=(2,1,0) u.v=(1.2+(-2.1)+(-1.0)) u.v=(2-2+0) u.v=0 A 32) |u|=3(u+v).(u+2v) |v|=4 u²+2.v.u+u.v+2.v² 3²+2.0+0+2.4² 9+0+0+32 41 C 33) u=(1,x,8) v=(2,1,-4) u.v=0 (1.2+x.1+(8.-4)=0 (2+x-32)=0 x-30=0 x=30 B 34) u=(0,-3,-1) i j k v=(2,4,0) 0-2 0 4 0 6 | i j k i j | u˄v=(4,-2,6) u˄v=|0-3-1 0-3| | 2 4 0 2 4| A 35) f(x)=e(cosx) u=cosx u'=-senx f'(x)=e(u).u' f'(x)=-senx.e(cosx) f(x)=ln(x²+4) u'=2x u=x²+4 f(x)=ln(u) f(x)=1/u.u' f'(x)=1/x²+4.2x f'(x)=2x/x²+4 f(x)=√3x+6 u'=3 f(x)=(3x+6)1/2 f(x)=3/2.1/u1/2 u=3x+6 f(x)=3/2√3x+6 f'(x)=(u)1/2 f'(x)=1/2.u-1/2.u' f'(x)=3/2.u-1/2 D 36) f(x)=sen(2x+4) u'=2 u=2x+4 f(x)=sen(u) f'(x)=cos(u).u' f'(x)=2cos(2x+4) f(x)=cos(3x+6) u'=3 u=3x+6 f(x)=cos(u) f'(x)=-sen(u).u' f'(x)=-sen(3x+6).3 f'(x)=-3sen(3x+6) f(x)=(x²+4x)³ u=x²+4x u'=2x+4 f(x)=(u)³ f'(x)=3u².2x+4 f'(x)=3(x²+4x).2x+4 f'(x)=(x²+4x)².(6x+12) C 37) F(x)=x³+4 (x³+4)'=f(x) f(x)=3x² F(x)=x^4+2 (x^4+2)'=f(x) f(x)=4x³ F(x)=x^5-2 (x^5-2)'=f(x) f(x)=5x^4 D 38) v=ds/dt=>ds=v.dt s=ʃv.dt 16=-2.1³+7.1²+c s=ʃ(14t-6t²).dt 16=-2+7+c s=14t²/2-6t³/3+c 16=5+c s=7t²-2t³+c c=11 s=7t²-2t³+11 B 39) ʃ(2x+cosx)dx = senx+2x²/2+c X²+senx+c A 40) ʃ(senx+4)dx ʃ(1/x+12)dx f(x)=ex -cosx+C+4x ln|x|+c+12x (ex)'=f(x) -cosx+4x+C ln|x|+12x+c C
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