calculus

Question 1

1.

Evaluate the integral.

11

-40

16

1

2 points

Question 2

1.

Find v ∙ u. v = 8i + 3j and u = 2i + 3j

16i + 9j

7

25

10i + 6j

2 points

Question 3

1.

Find the length and direction (when defined) of u × v.

u = - i + j + k, v = i + j + 2k

2 ; - i + j - k

2 ; i + j - k

8; i - j - k

8; i - j + k

2 points

Question 4

1.

Find the general solution for the differential equation.

= 15x2

y = 15x3 + C

y = + C

y = x3 + C

y = 5x3 + C

2 points

Question 5

1.

Find fx, fy, and fz. f(x ,y, z) = sin (xy) cos (yz2)

fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2) - z2 sin (xy) sin (yz2); fz = 2yz sin (xy) sin (yz2)

fx = y cos (xy) cos (yz2); fy = z2 sin (xy) sin (yz2)- x cos (xy) cos (yz2); fz = 2yz sin (xy) sin (yz2)

fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2); fz = -2yz sin (xy) sin (yz2)

fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2) - z2 sin (xy) sin (yz2); fz = - 2yz sin (xy) sin (yz2)

2 points

Question 6

1.

Find fx, fy, and fz. f(x, y, z) = x2y + y2z + xz2

fx = 2xy; fy = x2 + 2yz; fz = y2 + 2xz

fx = 2xy + z2; fy = x2 + 2yz; fz = y2 + 2xz

fx = 2xy + z2; fy = x2 + yz; fz = y2 + xz

fx = 2y + z2; fy = x2 + 2z; fz = y2 + 2x

2 points

Question 7

1.

Find the length and direction (when defined) of u × v. u = 5i + 3j , v = i - j

8; -8k

8; -k

2; -2k

2; 2k

2 points

Question 8

1.

Write the first four elements of the sequence.

n

, - , , -

, , ,

, , ,

1, , ,

2 points

Question 9

1.

Find the general solution for the differential equation.

= x - 15

y = - 15x + C

y = - x + C

y = x3 - 15x + C

y = 2x2 - 15 + C

2 points

Question 10

1.

Find the integral.

(2t + 5)4 + C

(2t + 5)4 + C

(2t + 5)4 + C

(2t + 5)4 + C

2 points

Question 11

1.

Find the integral.

(6x - 7)3/2 + C

(6x - 7)3/2 + C

(6x - 7)3/2 + C

(6x - 7)3/2 + C

2 points

Question 12

1.

Find the integral.

+ C

+ C

+ C

+ C

2 points

Question 13

1.

Write the first four elements of the sequence.

0, , ,

0, , ,

ln 2, , ,

, , ,

2 points

Question 14

1.

Find fx, fy, and fz. f(x, y, z) = z(ex)y

fx = zxexy; fy = zyexy; fz = exy

fx = zyexy; fy = zxexy; fz = exy

fx = zyexy; fy = zxexy; fz = zexy

fx = zexy; fy = zexy; fz = exy

2 points

Question 15

1.

Evaluate the double integral over the given region.

R =

π

2 points

Question 16

1.

Find and . f(x, y) = (4x4y3 + 10)2

= 16x3y3; = 12x4y2

= 2(4x4y3 + 10); = 2(4x4y3 + 10)

= 24x4y2(4x4y3 + 10); = 32x3y3(4x4y3 + 10)

= 32x3y3(4x4y3 + 10); = 24x4y2(4x4y3 + 10)

2 points

Question 17

1.

Find the general solution for the differential equation.

= 4e3x

y = 12e3x + C

y = e3x + C

y = e3x + C

y = 4e3x + C

2 points

Question 18

1.

Find the length and direction (when defined) of u × v. u = -3i - 8i - 4k, v = 0

0; no direction

0; -3i - 8i - 4k

; (-3i - 8i - 4k)

0; (-3i - 8i - 4k)

2 points

Question 19

1.

Find the general solution for the differential equation.

- 6x2 = 4

y = -2x3 + 4x + C

y = 2x3 + 4x + C

y = 2x3 - 2x + C

y = 2x3 + 2x + C

2 points

Question 20

1.

Find the angle between u and v in radians. u = 10i + 6j + 6k, v = 7i + 2j + 4k

1.12

0.23

1.48

1.34

2 points

Question 21

1.

Find the length and direction (when defined) of u × v. u = 2i + 2j - k, v = -i + k

3; i + j - k

9; i - j + k

3; i - j + k

9; i + j - k

2 points

Question 22

1.

Find the integral.

+ C

+ C

+ C

+ C

2 points

Question 23

1.

Find and . f(x, y) = x3 + 9x2y + 2xy3

= 3x2; = 9x2 + 6xy2

= x2 + 9xy + 2y3; = 9x2 + 2xy2

= 3x2 + 2xy + 2y3; = 9x2 + 3xy2

= 3x2 + 18xy + 2y3; = 9x2 + 6xy2

2 points

Question 24

1.

Evaluate the double integral over the given region.

R = {(x, y): 1 ≤ x ≤ 8, 7 ≤ y ≤ 9}

1008

504

672

336

2 points

Question 25

1.

Evaluate the integral.

1080

4320

- 5400

- 2880

2 points

Question 26

1.

Find and . f(x, y) = 10x - 4y2 - 2

= 8; = -8y - 2

= 10; = -8y

= -8y; = 10

= 10x; = -8y

2 points

Question 27

1.

Find fx, fy, and fz. f(x, y, z) = ln (xy)z

fx = ; fy = ; fz = ln (xy)

fx = - ; fy = - ; fz = ln (xy)

fx = z ln ; fy = z ln ; fz = ln (xy)

fx = ; fy = ; fz = z ln (xy)z - 1

2 points

Question 28

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

2 points

Question 29

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

(e5 - e3 - e2 - 1)

(e5 - e3 - e2 + 1)

(e5 - e3 - e2 - 1)

(e5 - e3 - e2 + 1)

2 points

Question 30

1.

Find and .

f(x, y) =

= - ; = -

= - ; = -

= ; =

= - ; = -

2 points

Question 31

1.

Find and . f(x, y) = sin2 (2xy2 - y)

= 4y2sin (2xy2 - y) cos (2xy2 - y); = (8xy - 2) sin (2xy2 - y) cos (2xy2 - y)

= 2sin (2xy2 - y) cos (2xy2 - y); = 2sin(2xy2 - y) cos(2xy2 - y)

= 4y2sin (2xy2 - y) cos (2xy2 - y); = 2sin (2xy2 - y) cos (2xy2 - y)

= 2sin (2xy2 - y) cos (2xy2 - y); = (8x - 2) sin (2xy2 - y) cos (2xy2 - y)

2 points

Question 32

1.

Find the angle between u and v in radians. u = 8i - 7j - 3k, v = 4i + 3j - 7k

1.23

1.57

1.41

0.34

2 points

Question 33

1.

Find the integral.

(2x + 5)4 + C

(2x + 5)4 + C

(2x + 5)4 + C

(2x + 5)4 + C

2 points

Question 34

1.

Evaluate the integral.

-

2 points

Question 35

1.

Find and .

f(x, y) = ln

= ; =

= -ln ; = ln

= - ; =

= -ln ; = ln

2 points

Question 36

1.

Find the length and direction (when defined) of u × v. u = 4i + 2j + 8k, v = -i - 2j - 2k

6 ; i + k

180; i + j + k

6 ; i - k

180; i + k

2 points

Question 37

1.

Write the first four elements of the sequence.

-1, 1, ,

1, , ,

0, , ,

, , ,

2 points

Question 38

1.

Evaluate the integral.

60

8

120

4

2 points

Question 39

1.

Evaluate the double integral over the given region.

R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ 1}

9π - 9

π

9π

2 points

Question 40

1.

Find the angle between u and v in radians. u = -4i + 10j - 6k, v = 10i + 7j - 9k

1.10

1.57

1.35

0.47

2 points

Question 41

1.

Find v ∙ u. v = -5i + 4j and u = 7i + 3j

-23

2i + 7j

-47

-35i + 12j

2 points

Question 42

1.

Evaluate the integral.

77

- 539

847

- 847

2 points

Question 43

1.

Find and . f(x, y) = ln yx

= ln y; = - xln y

= xln y; = -

= 0; = -

= ln y; =

2 points

Question 44

1.

Find and . f(x, y) = xye-y

= ye-y; = xe-y

= ye-y; = xe-y(1 - y)

= ye-y; = - xye-y

= ye-y; = xe-y(y - 1)

2 points

Question 45

1.

Find fx, fy, and fz. f(x, y, z) = xz

fx = z ; fy = - ; fz = x

fx = z ; fy = ; fz = x

fx = z ; fy = - ; fz = x

fx = z ; fy = ; fz = x

2 points

Question 46

1.

Find the length and direction (when defined) of u × v. u = 6i, v = 6j

36; -k

36; k

36; 36k

6; 6k

2 points

Question 47

1.

Find the length and direction (when defined) of u × v. u = -4i + 3j - 5k, v = 8i - 6j + 10k

0; no direction

0; 4i- 3j + 5k

5 ; (4i - 3j + 5k)

5 ; (4i - 3j + 5k)

2 points

Question 48

1.

Evaluate the double integral over the given region.

R = {(x, y): 9 ≤ x ≤ 10, 9 ≤ y ≤ 10}

2

2

ln

2 points

Question 49

1.

Find and .

f(x, y) =

= ; = -

= ; = -

= ; =

= - ; = -

2 points

Question 50

1.

Find the general solution for the differential equation.

= 18x2 - 14x

y = 6x3 - 14x2 + C

y = 6x3 - 7x2 + C

y = 18x3 - 7x2 + C

y = 18x3 - 14x2 + C

2 points