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