Trabalhos - unip

20. B
AB/|AB|= -1,1 / √2
AB/|AB|= (-1 / √2 , 1 / √2)

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

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

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

24.A a= f` (x)= f` (-2)= 3x² = 3(4) = 12 a= 12

25.A f`(x)= (e^x)` sen2x + (sen2x)` e^x f`(x)= e^x sen2x + (2 cos2x) e^x f`(0)= e^0 . sen 2(0) + 2 cos 2(0) . e^0 f`(0)= 1 . sen0 + 2 cos0 . 1 f`(0)= 1 . 0 + 2 . 1 f`(0)= 0 + 2 f`(0)= 2

26.E
I. u . v = (2,-4) . (0,-3)= (0+12) u . v = 12 (tem alguma caisa escrita que não da para entender)

II. u = (2,4) v = (0,3)

u . v = (2,4) . (0,3) = (0 + 12) u . v = 12

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

28.A
A lelo = |u^v| = √84 = 2 √21
A lelo = 2 √21 u ^ v = 2j - 8k + 4k + 8i = 8i + 2j – 4k u ^ v = (8,2,-4)
|u ^ v| = √(8)^2 + (2)^2 + (-4)^2
|u ^ v| = √84

29.E
A do triangulo = ½ |u ^ v| = ½ . 3 = 1,5
A do triangula = 1,5 u.a.

|u ^ v|= |u| . |v| . sen30°
|u ^ v|= 2 . 3 . ½
|u ^ v|= 3

30.B w . u = 0
(2,-4,10) . (1,-2,-1) =0
2 + 8 -10 = 0
0 = 0

w . v = 0
(2,-4,10) . (2,1,0) = 0
4 – 4 + 0 = 0
0 = 0

|w| = 2√30
√(2)² + (-4)² + (10)² = 2√30
√4 + 16 + 100 = 2√30
√120 = 2√30
2√30 = 2√30

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

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

33.B
Se u é ortogonal a v então u . v = 0
(1,x,8) . (2,1,-4) = 0
2 + x – 32 = 0 x = 32 – 2 x = 30

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

35.D
I. f`(x) = e^cosx . (cosx)` = e^cosx . (-senx) = -senx e^cosx

II. f`(x) = ln (x² + 4) = f`(x) = (x² + 4)` / (x² + 4) = 2x / (x² + 4)

III. f(x) = √3x + 6 f`(x) = (3x + 6)^1/2 = ½(3x + 6)^-1/2 . (3x + 6)` = ½(3x + 6) (3) f`(x) = 3/2(3x + 6)^1/2 = 3/2√(3x + 6)

36.C
I. f(x) = sen(2x + 4) = f`(x)