sadasd

20)
AB= B-A= (-2,1)-(-1,0)
AB= (-1,1)
|AB|= raiz de 2
AB/|AB|= -1,1/raiz de 2
AB/|AB|= (-1/raiz de 2, 1/raiz de 2)
AB/|AB|= (-raiz de 2/2, raiz de 2/2)

21)
V(2)= 6(2)³+1,5(2)
V(2)= 48+3
V(2)= 51 L

22) dv/dt=18t²+1,5 dv/dt= 18(2)²+1,5= 72+1,5 dv/dt= 73,5 L/min

23) y'= (x+16)'senx+(senx)'(x+16) y'= 1senx+(cosx).(x+16) y'= senx+(x+16)cosx

24) a= f'(x0)= f'(-2)= 3x²= 3(-2)²= 3(4)=12 a= 12

25) f'(x)= (e^x)'sen2x+(sen2x)'e^x f'(x)= e^.xsen2x+(2cos2x)e^x f'(0)= e^0.sen(0)+2cos2(0).e^0 f'(0)= 1.sen0+2cos0.1 f'(0)= 1.0+2.1 f'(0)= 0+2 f'(0)=2 26)
I) u.v= (2,-4).(0,-3)=(0,12) o produto escalar deveria ser igual a 12
III) u.v= (2,4).(0,3)= (0,12) o produto escalar deveria ser igual a 12

27)
2(2,-4).5(1,-2)= (4,-8).(5,-10)= (20+80)= 100

28)
Alelo= |u^v|= raiz de 84= 2 raiz de 21
Alelo= 2 raiz de 2 u^v= 2j-8k+4k+8i= 8i+2j u^v= (8,2,-4)
|u.v|= (raiz de(8)^2+(2)^2+(-4)^2)
|u.v|= (raiz de 6a+4+16)= raiz de 84= 2 raiz de 21

29)
|u.v|= |u|.|v|.sen30º
|u.v|= 2.3.1/2
|u.v|= 3
Atrian= 1/2.|u^v|= 1/2.3= 3/2= 1,5 u.a

30)
w.u= 0
(2,-4,10).(1,-2,-1)=0
2+8-10= 0
0=0 (v)
w.v=0
(2,-4,10).(2,1,0)=0
4-4+0=0
0= 0
|w|= 2 raiz de 30
(raiz de (2)^2+(-4)^2+(10)^2)= 2 raiz de 30
(raiz de 4+16+100)= 2 raiz de 30 raiz de 20= 2 raiz de 30
2 raiz de 30 = 2 raiz de 30

31)
u.v= (1,-2,-1).(2,1,0)=0
u.v= 2-2+0
u.v= 0

32)
(u+v).(u+2v)
|u|^2+2uv+vu+2|v|²
|u|^2+3uv=2|v|²
(3)²+3(0)+2(4)²
9+0+32= 41

33)
Se u.v=0
(1,x,8).(2,1,-4)
2+x=32=0 x= 32-2 x= 30

34) u^v= -2j+6k+4i u^v= (4,-2,6)

35)
I) Verdadeira f(x)= e^cosx f'(x)= e^cosx. (cosx)'= e^cosx. (-senx)= -senx.e^cosx
II) Verdadeira f(x)= ln(x²+4) f'(x)= x²+4)'/(x²+4)= 2x/(x²+4)
III) Verdadeira f(x)= (raiz de 3x+6)= (3x+6)^1/2 f'(x)=1/2(3x+6)^-1/2.(3) f'(x)= 1/2(3x+6)^-1/2.(3)= 3/2(3x+6)^1/2= 3/2 raiz de 3x+6

37)
I) Verdadeira f(x)=x³+4 f'(x)-3x²
II) Verdadeira f(x)= x^4+2 f'(x)= 4x³
III) Verdadeira f(x)= x^5-2 f'(x)= 5x^4