Estudos diciplinares 2

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23 letra “ b ”

Y = ( x + 16) * senxy´= senx + D (sen u) = sen x + u´ * cos uu = x + 16 u´= 1 y´= senx + 1 * ( x + 16) * cosxy´= senx + ( x + 16) * cosx

24 falta “ a ”

F(x) = x^3 - 8

F’(x) = 3 (x^2)

F’(-2) = 3 (-2)^2

F’(-2) = 3 * 4

F’(-2) = 12

25 letra “ a ”

f(x) = e^x * sen (2x)=

f'(0)= e^x * sen (2x)=

f'(0)= e^x * cos 2=

f'(0) = 2

26 letra “e”

II) u = (2 ,-4) v = (0, -3)u * v = 2 * 0 + (-4) * (-3)u * v = 0 + 12u * v = 12

27 letra “C”

Vetor u e v

u = ( 2 , -4 ) v = ( 1 , -2 )

2 * u = 2 * ( 2 , -4 ) = ( 4 , -8 ) = √ 16 + 64 = √ 80

5 * v = 5 * ( 1 , -2 ) = ( 5 , 10 ) = √ 25 + 100 = √ 125

√ 80 * √ 124 = √ 10.000 = 100

28 letra “a”

Vetores u e v

U = (2, -4, 2)

V = (1, -4 , 0)

|i , j , k| i , j

|2 , -4, 2| 2 , -4

|1 , -4, 0| 1 , -4

4k + 8i + 0 + 0 + 2j – 8k =

8i , 2 j , -4

|i , j , k |

|8 , 2 , -4|

A = √ 8 ^ 2 + 2 ^ 2(-4) ^ 2

A = √ 64 + 4 + 16

A = √ 84

A = 2 √ 21

84|2

42|2

21|38

7|7

1|

29 letra “e”

Vetores e modulos

|u| = 2 |v| = 3 |u| * |v|=

SEN 30 = 2 * 3 = 6 * SEN 30 6 * 1/2 = 3/2 =

1,5 unidade de area

30 letra “B”

d = √ 2 ^ 2 + ( -4 ) ^ 2 + 10 ^ 2 =

d = √ 4 + 16 + 100 =

d = √ 4 * 30

d = 2√ 30

31 letra “ a ”

u = ( 1, -2, -1) v = ( 2, 1, 0)u * v = ( 1, -2, -1 ) * ( 2, 1, 0)u * v = 2 * 1 + (-2) * 1 + (-1) + 0u * v = 2 – 2 + 0u * v = 0

32 letra “c”

vetores

(u + v) * (u + 2 * v)

=|u| ^ 2 + 2 |v| * |u| + |u||v| + 2 * |v| ^ 2

= 3 ^ 2 + 2 * 0 + 0 + 2 * 4 ^2

= 9 + 0 + 32

= 41

33 letra “b”

u = (1 , x, 8) e v = (2, 1, -4)

u * v = 0

(1 , x, 8) * ( 2, 1, -4) = 0

2 + x – 32 = 0

X – 30 = 0

X = 30

34 letra “ a ”

vetores

u = (0 , -3 , -1) e v =( 2, 4, 0)

u * v = i j k i j0 -3 -1

0 -3 0 - 2j + 0 – 0 + 4i + 6k 2 4 0 2 4 4i – 2j + 6k ou u * v = ( 4 ,-2, 6)

35 letra “ D ”

I) f (x) = e ^ cos x u = cos x

f (x) = e ^ u dv = sen x

f(x)’ = e ^ u * du

f(x)’ = e ^cos x * ( sen x)

II) f(x) = ln ( x ^ 2 + 4 ) u = x ^ + 4

f(x) = ln u du = 2x

f(x)’ = 1/u * du

f(x)’ = 1/ x ^ 2 + 4 * 2x =

f(x)’ = 2x / x ^ 2 + 4

III) f(x) = √ 3 x + 6 u = 3x + 6

f(x) = u ^1/2 du = 3

f(x)’ = 1 / 2 u ^ 1 / 2 - 1

f(x)’ = 1 / 2 u ^ -1 / 2 * du

f(x)’ = 1 / 2 √ u * du

f(x)’ = 1 / 2 √ 3 x + 6 * 3

f(x)’ = 3 / 2 √ 3 x + 6

36 letra “ C ”

I) f(x) = sen ( 2x + 4 )

f(x) = sen u

f(x)’ = cos u * du

f(x)’ = cos ( 2x + 4 ) * 2

f(x)’ = 2 * cos ( 2x + 4 )

(Falsa)

II) f(x) = cos ( 3x + 6 ) u = 3x + 6

f(x)’ = cos u du = 3

f(x)’ = - sen u * du

f(x)’ = - sen ( 3x + 6 ) * 3

f(x)’ = -3 sen ( 3x + 6 )