Calculus homework

Question 1

1.  

Evaluate using integration by parts.

		ln x -  + C
		x2 ln x -  + C
		x2 ln x - x2 + C
		x ln x - x + C

2 points  

Question 2

1.  

Evaluate using integration by parts.

		x2e2x - xe2x + e2x + C
		x2e2x - xe2x + e2x + C
		x2e2x - xe2x + C
		x2e2x - xe2x + e2x + C

2 points  

Question 3

1.  

Evaluate. Assume u > 0 when ln u appears.   dy

		2e4y + C
		e4y + C
		4e4y + C
		e4y + C

2 points  

Question 4

1.  

Find the particular solution determined by the given condition. f'(x) = 6x2 - 4x + 21; f(1) = 17

		f(x) = 2x3 - 4x2 + 21x - 2
		f(x) = 6x3 - 4x2 + 21x - 6
		f(x) = 2x3 - 2x2 + 21x + 4
		f(x) = 2x3 - 2x2 + 21x - 4

2 points  

Question 5

1.  

Find the particular solution determined by the given condition. y' =  ; y = 21 when x = 1

		y = 5 ln x + 21
		y = ln x + 19
		y = 5 ln x + 2.5
		y = ln x + 21

2 points  

Question 6

1.  

Determine if the function is a solution to the given differential equation. y = x ln x - 4x + 5; y'' -  = 0.

		Yes
		No

2 points  

Question 7

1.  

Evaluate using integration by parts.

		(x2 - x) ln (16x) -  + 2x + C
		(x2 - x) ln (16x) -  + x + C
		ln (16x) -  + x + C
		(x2 - x) ln (16x) - x2 + x + C

2 points  

Question 8

1.  

Find the general solution for the differential equation.  = 4P

		P = 4eCt
		P = Ce4t
		P = Ce-4t
		P = Cet

2 points  

Question 9

1.  

Evaluate. Assume u > 0 when ln u appears.   dt

		e-7t2 + C
		-  e-7t2 + C
		e-7t2 + C
		-  e-7t2 + C

2 points  

Question 10

1.  

Find the general solution for the differential equation. y ' = 72x2 - 20x

		72x3 - 20x2 + C
		24x3 - 20x2 + C
		72x3 - 10x2 + C
		24x3 - 10x2 + C

2 points  

Question 11

1.  

Find the general solution for the differential equation. y ' = x - 16

		2x2 - 16 + C
		- 16x + C
		- x + C
		x3 - 16x + C

2 points  

Question 12

1.  

Evaluate using integration by parts. e4xdx

		(x - 8) e4x -  e4x + C
		(x - 8) e4x +  e4x + C
		4(x - 8) e4x - 16 e4x + C
		(x - 8) e4x - e4x + C

2 points  

Question 13

1.  

Evaluate using integration by parts. dx

		5x(2x + 3)1/2 + (2x + 3)3/2 + C
		5x(2x + 3)1/2 - (2x + 3)3/2 + C
		x(2x + 3)1/2 - (2x + 3)3/2 + C
		5x(2x + 3)1/2 - (2x + 3)3/2 + C

2 points  

Question 14

1.  

Write the first four elements of the sequence.  n

		0, 2, ,
		2, , ,
		1, , ,
		0, 1, ,

2 points  

Question 15

1.  

Evaluate. Assume u > 0 when ln u appears.   dx

		+ C
		+ C
		+ C
		(ln 6x)2 + C

2 points  

Question 16

1.  

Evaluate. Assume u > 0 when ln u appears.   dp

		e5p2+ C
		-  e5p2 + C
		7e5p2 + C
		-7e5p2 + C

2 points  

Question 17

1.  

Evaluate. Assume u > 0 when ln u appears.   dy

		ln  + C
		18 ln  + C
		19 ln  + C
		ln  + C

2 points  

Question 18

1.  

Evaluate using integration by parts. dx

		x(ln 2x)2 - 2 ln (2x) + C
		ln (2x)2 - 2x ln (2x) - 2x + C
		x(ln 2x)2 + 2x ln (2x) + 2x + C
		x(ln 2x)2 - 2x ln (2x) + 2x + C

2 points  

Question 19

1.  

Evaluate using integration by parts. ln x dx

		x2ln x - x2 + C
		ln x - x2 + C
		x2ln x - x2 + 5x + C
		x2ln x - x2 - 5x + C

2 points  

Question 20

1.  

Find the general solution for the differential equation. y ' = 2e3x

		2e3x + C
		e3x + C
		6e3x + C
		e3x + C

2 points  

Question 21

1.  

Determine if the function is a solution to the given differential equation. y = ex + 3xex; y'' - 2y' + y = 0.

		Yes
		No

2 points  

Question 22

1.  

Evaluate. Assume u > 0 when ln u appears. 

		- (7x2 + 3)-6 + C
		- (7x2 + 3)-6 + C
		- (7x2 + 3)-4 + C
		- (7x2 + 3)-4 + C

2 points  

Question 23

1.  

Evaluate. Assume u > 0 when ln u appears.   dy

		-  + C
		-  + C
		+ C
		+ C

2 points  

Question 24

1.  

Find the general solution for the differential equation. y' =  - x4 + x6

		y = -4 - 4x3 + 6x5 + C
		y = 2 ln x - x6 + x8 + C
		y = 2 ln x - x5 + x7 + C
		y =   - x4 + x6 + C

2 points  

Question 25

1.  

Determine if the function is a solution to the given differential equation. y = 3e2x + xe2x; y'' + 2y' + 1 = 0.

		Yes
		No

2 points  

Question 26

1.  

Find the particular solution determined by the given condition. f'(x) = 3x2 - 2x; f(0) = 18 

		f(x) = 3x3 + 2x2 + 18
		f(x) = x3 - x2 + 18
		f(x) = x3 + 2x2 + 18
		f(x) = 3x3 + x2 + 18

2 points  

Question 27

1.  

Evaluate using integration by parts.

		x1 - n ln x + x1 - n + C
		ln x - x1 - n + C
		x1 - n ln x - x2 - n + C
		x1 - n ln x - x1 - n + C

2 points  

Question 28

1.  

Evaluate using integration by parts. ln 7x dx

		x5 ln 7x -  x5 + C
		ln 7x -  x5 + C
		x5 ln 7x -  x6 + C
		x5 ln 7x +  x5 + C

2 points  

Question 29

1.  

Evaluate. Assume u > 0 when ln u appears.   dx

		-11 e-4x3 + C
		12 e-4x3 + C
		e-4x3 + C
		-  e-4x3 + C

2 points  

Question 30

1.  

Find the particular solution determined by the given condition. f'(x) = x4/5 + x; f(1) = -6

		f(x) = x1/5 + x2 -
		f(x) = x9/5 + x2 -
		f(x) = x9/5 - x2 +
		f(x) = x9/5 + 2x2 +

2 points  

Question 31

1.  

Evaluate using integration by parts.

		7x ln x - x + C
		x ln 7x + x + C
		x ln 7x - 7x + C
		x ln 7x - x + C

2 points  

Question 32

1.  

Evaluate using integration by parts.

		- x e-5x - e-5x + C
		-10x e-5x - 80 e-5x + C
		x e-5x + e-5x + C
		-  x e-5x -  e-5x + C

2 points  

Question 33

1.  

Determine if the function is a solution to the given differential equation. y = 2e2x + xe2x; y'' - 2y' + 1 = 0.

		No
		Yes

2 points  

Question 34

1.  

Evaluate. Assume u > 0 when ln u appears.   dx

		+ C
		(x5 - 4)5 + C
		+ C
		+ C

2 points  

Question 35

1.  

Evaluate. Assume u > 0 when ln u appears. 

		ln  + C
		20 ln  + C
		20 ln(4x5 + 8) + C
		ln  + C

2 points  

Question 36

1.  

Determine if the function is a solution to the given differential equation. y = e-x + 2xe-x; y'' + 2y' + y = 0.

		No
		Yes

2 points  

Question 37

1.  

Find the general solution for the differential equation. y ' - 12x2 = 20

		- 4x3 + 20x + C
		4x3 + 10x + C
		4x3 + 20x + C
		4x3 - 10x + C

2 points  

Question 38

1.  

Evaluate using integration by parts. dx

		x3/2 ln  + x3/2 + C
		x3/2 ln  - x3/2 + C
		x3/2 ln  - x3/2 + C
		5x3/2 ln  - 5x3/2 + C

2 points  

Question 39

1.  

Find the particular solution determined by the given condition.  = 5H; where H = 6.5 when t = 0

		H(t) = e5t + 6.5
		H(t) = 5e6.5t
		H(t) = 6.5e5t
		H(t) = 6.5e5t + 6.5

2 points  

Question 40

1.  

Evaluate using integration by parts.

		6ex - 6xex + C
		6ex - ex + C
		6xex - 6ex + C
		xex - 6ex + C

2 points  

Question 41

1.  

Determine if the function is a solution to the given differential equation. y = 4x ln x + 4x + 5; y'' -  = 0.

		Yes
		No

2 points  

Question 42

1.  

Evaluate using integration by parts.  dx

		- x(3 - x)3/2 + (3 - x)5/2 + C
		x(3 - x)3/2 + (3 - x)5/2 + C
		- x(3 - x)3/2 - (3 - x)5/2 + C
		- x(3 - x)3/2 - (3 - x)5/2 + C

2 points  

Question 43

1.  

Find the general solution for the differential equation.  = 7y

		y = Cex
		y = Ce-7x
		y = Ce7x
		y = 7eCx

2 points  

Question 44

1.  

Evaluate using integration by parts. dx

		x4(ln 4x)2 - 39x3 ln 4x + C
		x4(ln 4x)2 + 39x4 ln 4x - x4 + C
		x4(ln 4x)2 - x4 ln 4x + x4 + C
		x4(ln 4x)2 - 39x4 ln 4x + x4 + C

2 points  

Question 45

1.  

Find the particular solution determined by the given condition.  = 0.24D; where D(0) = 200

		D(t) = 200e0.24t
		D(t) = 200e0.24t + 200
		D(t) = e48t
		D(t) = 0.24e200t

2 points  

Question 46

1.  

Evaluate using integration by parts. dx

		x2(x2 + 8)3/2 - (x2 + 8)5/2 + C
		x2(x2 + 8)3/2 + (x2 + 8)5/2 + C
		x(x2 + 8)3/2 - (x2 + 8)7/2 + C
		2x2(x2 + 8)3/2 - 2(x2 + 8)5/2 + C

2 points  

Question 47

1.  

Evaluate using integration by parts. dx

		x(3x - 10)3/2 - (3x - 10)5/2 + C
		x(3x - 10)3/2 - (3x - 10)5/2 + C
		x(3x - 10)3/2 - (3x - 10)5/2 + C
		x(3x - 10)3/2 + (3x - 10)5/2 + C

2 points  

Question 48

1.  

Find the general solution for the differential equation. y ' = 18x2

		x3 + C
		6x3 + C
		18x3 + C
		+ C

2 points  

Question 49

1.  

Find the particular solution determined by the given condition. y' = 4x + 10; y = -21 when x = 0

		y = 4x2 + 10x - 10.5
		y = 4x2 + 10x - 21
		y = 2x2 + 10x - 10.5
		y = 2x2 + 10x - 21

2 points  

Question 50

1.  

Evaluate using integration by parts. dx

		+ C
		+ C
		7ex(x + 1)2 + C
		-  - 7ex + C