Calculus homework

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Question 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

Evaluate using integration by parts.

x2e2x - xe2x + e2x + C

x2e2x - xe2x + C

x2e2x - xe2x + e2x + C

2 points

Question 3

Evaluate. Assume u > 0 when ln u appears.

2e4y + C

e4y + C

4e4y + C

e4y + C

2 points

Question 4

Find the particular solution determined by the given condition.

fʹ(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

Find the particular solution determined by the given condition.

yʹ = ; 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

Determine if the function is a solution to the given differential equation.

y = x ln x - 4x + 5; yʹʹ - = 0.

Yes

2 points

Question 7

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

Find the general solution for the differential equation.

= 4P

P = 4eCt

P = Ce4t

P = Ce-4t

P = Cet

2 points

Question 9

Evaluate. Assume u > 0 when ln u appears.

e-7t2 + C

- e-7t2 + C

e-7t2 + C

- e-7t2 + C

2 points

Question 10

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

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

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

Evaluate using integration by parts.

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

Write the first four elements of the sequence.

0, 2, ,

2, , ,

1, , ,

0, 1, ,

2 points

Question 15

Evaluate. Assume u > 0 when ln u appears.

+ C

(ln 6x)2 + C

2 points

Question 16

Evaluate. Assume u > 0 when ln u appears.

e5p2+ C

- e5p2 + C

7e5p2 + C

-7e5p2 + C

2 points

Question 17

Evaluate. Assume u > 0 when ln u appears.

ln + C

18 ln + C

19 ln + C

ln + C

2 points

Question 18

Evaluate using integration by parts.

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

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

Find the general solution for the differential equation.

y ' = 2e3x

2e3x + C

e3x + C

6e3x + C

e3x + C

2 points

Question 21

Determine if the function is a solution to the given differential equation.

y = ex + 3xex; yʹʹ - 2yʹ + y = 0.

Yes

2 points

Question 22

Evaluate. Assume u > 0 when ln u appears.

- (7x2 + 3)-6 + C

- (7x2 + 3)-4 + C

2 points

Question 23

Evaluate. Assume u > 0 when ln u appears.

- + C

+ C

2 points

Question 24

Find the general solution for the differential equation.

yʹ = - 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

Determine if the function is a solution to the given differential equation.

y = 3e2x + xe2x; yʹʹ + 2yʹ + 1 = 0.

Yes

2 points

Question 26

Find the particular solution determined by the given condition.

fʹ(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

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

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

Evaluate. Assume u > 0 when ln u appears.

-11 e-4x3 + C

12 e-4x3 + C

e-4x3 + C

- e-4x3 + C

2 points

Question 30

Find the particular solution determined by the given condition.

fʹ(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

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

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

Determine if the function is a solution to the given differential equation.

y = 2e2x + xe2x; yʹʹ - 2yʹ + 1 = 0.

Yes

2 points

Question 34

Evaluate. Assume u > 0 when ln u appears.

+ C

(x5 - 4)5 + C

+ C

2 points

Question 35

Evaluate. Assume u > 0 when ln u appears.

ln + C

20 ln + C

20 ln(4x5 + 8) + C

ln + C

2 points

Question 36

Determine if the function is a solution to the given differential equation.

y = e-x + 2xe-x; yʹʹ + 2yʹ + y = 0.

Yes

2 points

Question 37

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

Evaluate using integration by parts.

x3/2 ln + x3/2 + C

x3/2 ln - x3/2 + C

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

2 points

Question 39

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

Evaluate using integration by parts.

6ex - 6xex + C

6ex - ex + C

6xex - 6ex + C

xex - 6ex + C

2 points

Question 41

Determine if the function is a solution to the given differential equation.

y = 4x ln x + 4x + 5; yʹʹ - = 0.

Yes

2 points

Question 42

Evaluate using integration by parts.

- 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

Find the general solution for the differential equation.

= 7y

y = Cex

y = Ce-7x

y = Ce7x

y = 7eCx

2 points

Question 44

Evaluate using integration by parts.

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

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

Evaluate using integration by parts.

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

Evaluate using integration by parts.

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

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

2 points

Question 48

Find the general solution for the differential equation.

y ' = 18x2

x3 + C

6x3 + C

18x3 + C

+ C

2 points

Question 49

Find the particular solution determined by the given condition.

yʹ = 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

Evaluate using integration by parts.

+ C

7ex(x + 1)2 + C

- - 7ex + C