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Worksheets

Final HUGE AP Review

Total questions: 178

Worksheet time: 1hrs 29mins

Name
Class
Date
1.
a)
b)
c)
d)
2.
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3.
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b)
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4.
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5.
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b)
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6.
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7.
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8.
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9.
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10.
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28.
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b)
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29.
a)
b)
c)
d)
30.

sec⁡(θ)=\sec\left(\theta\right)=  

a)

1cos⁡(θ)=1x\frac{1}{\cos\left(\theta\right)}=\frac{1}{x}  

b)

1sin⁡(θ)=1y\frac{1}{\sin\left(\theta\right)}=\frac{1}{y}  

c)

sin⁡(θ)cos⁡(θ)=yx\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{y}{x}  

d)

cos⁡(θ)sin⁡(θ)=xy\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}=\frac{x}{y}  

31.

csc⁡(θ)=\csc\left(\theta\right)=  

a)

1cos⁡(θ)=1x\frac{1}{\cos\left(\theta\right)}=\frac{1}{x}  

b)

1sin⁡(θ)=1y\frac{1}{\sin\left(\theta\right)}=\frac{1}{y}  

c)

sin⁡(θ)cos⁡(θ)=yx\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{y}{x}  

d)

cos⁡(θ)sin⁡(θ)=xy\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}=\frac{x}{y}  

32.

tan⁡(θ)=\tan\left(\theta\right)=  

a)

1cos⁡(θ)=1x\frac{1}{\cos\left(\theta\right)}=\frac{1}{x}  

b)

1sin⁡(θ)=1y\frac{1}{\sin\left(\theta\right)}=\frac{1}{y}  

c)

sin⁡(θ)cos⁡(θ)=yx\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{y}{x}  

d)

cos⁡(θ)sin⁡(θ)=xy\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}=\frac{x}{y}  

33.

cot⁡(θ)=\cot\left(\theta\right)=  

a)

1cos⁡(θ)=1x\frac{1}{\cos\left(\theta\right)}=\frac{1}{x}  

b)

1sin⁡(θ)=1y\frac{1}{\sin\left(\theta\right)}=\frac{1}{y}  

c)

sin⁡(θ)cos⁡(θ)=yx\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{y}{x}  

d)

cos⁡(θ)sin⁡(θ)=xy\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}=\frac{x}{y}  

34.
a)

1

b)

3

c)

DNE

d)

5

35.
a)

1

b)

3

c)

DNE

d)

0

36.
a)

3

b)

1

c)

DNE

d)

5

37.
a)

4

b)

1

c)

DNE

d)

2

38.
a)

4

b)

2

c)

1

d)

3

39.
a)

4

b)

2

c)

1

d)

DNE

40.
a)

True

b)

False

41.
a)

True

b)

False

42.
a)

3

b)

1

c)

DNE

d)

Undefined

43.
a)

1

b)

3

c)

DNE

d)

Undefined

44.
a)

DNE

b)

Undefined

c)

1

d)

3

45.
a)

2

b)

1

c)

DNE

d)

Undefined

46.
a)

2

b)

1

c)

Undefined

d)

DNE

47.
a)

Big infinity over little infinity equals infinity

b)

Little infinity over big infinity equals zero

c)

Same infinity over same infinity equals ratio

d)

Factor and cancel

48.
a)

Big infinity over little infinity equals infinity

b)

Little infinity over big infinity equals zero

c)

Same infinity over same infinity equals ratio of 1/1=1

d)

Factor and cancel

49.
a)

Big infinity over little infinity equals infinity

b)

Little infinity over big infinity equals zero

c)

Same infinity over same infinity equals ratio equals 1/e

d)

Factor and cancel

50.
a)

Big infinity over little infinity equals infinity

b)

Little infinity over big infinity equals zero

c)

Same infinity over same infinity equals ratio equals 2/3

d)

Factor and cancel

51.
a)

Big infinity over little infinity equals infinity

b)

Little infinity over big infinity equals zero

c)

Same infinity over same infinity equals ratio equals 3/1

d)

Same infinity over same infinity equals ration 9/1

52.
a)

0

b)

1

c)

cos(x)

d)

sin(x)

53.
a)

0

b)

1

c)

cos(x)

d)

sin(x)

54.
a)

Little infinity over big infinity equals zero

b)

Big infinity over little infinity equals infinity

c)

Same infinity over same infinity equals 1 over 1

55.
a)

Little infinity over big infinity equals zero

b)

Big infinity over little infinity equals infinity

c)

Same infinity over same infinity equals 1 over 1

56.
a)

Little infinity over big infinity equals zero

b)

Big infinity over little infinity equals infinity

c)

Same infinity over same infinity equals 1 over 1

57.
a)

1

b)

5

c)

0

d)

1/5

58.
a)

Check Left, Check Right, See if Equal

b)

Multiply by conjugate

c)

Graph

d)

Set equal, solve for constant

59.
a)

Check Left, Check Right, See if Equal

b)

Multiply by conjugate

c)

Graph

d)

Set equal, solve for constant

60.

When using the Intermediate Value Theorem on  f(x)f\left(x\right)  , you must first write

a)

Since  f(x)f\left(x\right)  is increasing

b)

Since  f(x)f\left(x\right)  is continous

c)

Since  f(x)>Lf\left(x\right)>L  

d)

Since  f(x)f\left(x\right)  is a function

61.

To find the horizontal asymptotes of f(x)f\left(x\right)  , you consider

a)

The limit of  f(x)f\left(x\right)  as x approaches positive and negative infinity

b)

Set the denominator of  f(x)f\left(x\right)  equal to zero, ignoring holes

c)

Find the holes by cancelling common factors

62.

To find the vertical  asymptotes of f(x)f\left(x\right)  , you consider

a)

The limit of  f(x)f\left(x\right)  as x approaches positive and negative infinity

b)

Set the denominator of  f(x)f\left(x\right)  equal to zero, ignoring holes

c)

Find the holes by cancelling common factors

63.

If  f(x)=5x−2x+3f\left(x\right)=\frac{5x-2}{x+3} , the vertical asymptote is 

a)

x=−3x=-3  

b)

x=3x=3  

c)

y=5y=5  

d)

y=−5y=-5  

64.

If  f(x)=5x−2x+3f\left(x\right)=\frac{5x-2}{x+3} , the horizontal asymptote is 

a)

x=−3x=-3  

b)

x=3x=3  

c)

y=5y=5  

d)

y=−5y=-5  

65.
a)

Find cosine of x=pi/3

b)

Limits to infinity - big infinity over little infinity

c)

Limit definition of the derivative question, find the derivative of cosine

d)

Graph and find the limit

66.
a)

Limit definition of the derivative - find the derivative of x3 at x=2

b)

Limits to infinity

c)

Graph, then find limit

d)

Factor and cancel

67.
a)
b)
c)
d)
68.
a)
b)
c)
d)
69.
a)
b)
c)
d)
70.
a)
b)
c)
d)
71.
a)
b)
c)
d)
72.
a)
b)
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73.
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b)
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74.
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b)
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75.
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b)
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76.
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b)
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77.
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b)
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78.
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b)
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79.
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b)
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80.
a)
b)
c)
d)
81.
a)
b)
c)
d)
82.
a)
b)
c)
d)
83.

If

f(x)=log⁡3(x)f\left(x\right)=\log_3\left(x\right)  , then ...

a)

f′(x)=1xln⁡(3)f'\left(x\right)=\frac{1}{x\ln\left(3\right)}  

b)

f′(x)=ln⁡(3)⋅3xf'\left(x\right)=\ln\left(3\right)\cdot3^x  

c)

f′(x)=13xf'\left(x\right)=\frac{1}{3x}  

d)

f′(x)=3xf'\left(x\right)=\frac{3}{x}  

84.

If f(x)=cos⁡(x3)f\left(x\right)=\cos\left(x^3\right)  , then  f′(x)=f'\left(x\right)=  

a)

f′(x)=−3x2sin⁡(x3)f'\left(x\right)=-3x^2\sin\left(x^3\right)  

b)

f′(x)=−sin⁡(x3)f'\left(x\right)=-\sin\left(x^3\right)  

c)

3x2cos⁡(x3)3x^2\cos\left(x^3\right)  

d)

f(x)=−3sin⁡(x3)f\left(x\right)=-3\sin\left(x^3\right)  

85.

If  m(x)=(f(x))5m\left(x\right)=\left(f\left(x\right)\right)^5  , then  m′(x)=m'\left(x\right)=  

a)

5(f(x))4f′(x)5\left(f\left(x\right)\right)^4f'\left(x\right)  

b)

5(f′(x))45\left(f'\left(x\right)\right)^4  

c)

5f(x)f′(x)5f\left(x\right)f'\left(x\right)  

d)

(f′(x))5\left(f'\left(x\right)\right)^5  

86.

If  h(x)=f(g(x))h\left(x\right)=f\left(g\left(x\right)\right)  , then  h′(x)=h'\left(x\right)=  

a)

f′(g(x))g′(x)f'\left(g\left(x\right)\right)g'\left(x\right)  

b)

f(g′(x))f\left(g'\left(x\right)\right)  

c)

f′(x)g(x)+f(x)g′(x)f'\left(x\right)g\left(x\right)+f\left(x\right)g'\left(x\right)  

d)

f′(g′(x))f'\left(g'\left(x\right)\right)  

87.

ddx(uv)\frac{d}{dx}\left(uv\right)  

a)

u′v+uv′u'v+uv'  

b)

u′v′u'v'  

c)

u′v−uv′u'v-uv'  

d)

uvuv  

88.

  ddx(uv)=\frac{d}{dx}\left(\frac{u}{v}\right)=  

a)

u′v−uv′v2\frac{u'v-uv'}{v^2}  

b)

u′v+uv′u'v+uv'  

c)

u′v′\frac{u'}{v'}  

d)

u′v−uv′u'v-uv'  

89.

If  h(x)=x2f(x)h\left(x\right)=x^2f\left(x\right)  , then  h′(x)=h'\left(x\right)=  

a)

h′(x)=2xf(x)+x2f′(x)h'\left(x\right)=2xf\left(x\right)+x^2f'\left(x\right)  

b)

h′(x)=2xf′(x)h'\left(x\right)=2xf'\left(x\right)  

c)

h′(x)=x2f(x)⋅f′(x)h'\left(x\right)=x^2f\left(x\right)\cdot f'\left(x\right)  

d)

f′(x)=2(f(x))f′(x)f'\left(x\right)=2\left(f\left(x\right)\right)f'\left(x\right)  

90.

If

f(x)=x3sin⁡(x)f\left(x\right)=\frac{x^3}{\sin\left(x\right)}  , then find  f′(x)f'\left(x\right)  

a)

3x2cos⁡(x)\frac{3x^2}{\cos\left(x\right)}  

b)

(3x2)(sin⁡(x))−(x3)(cos⁡(x))(sin⁡(x))2\frac{\left(3x^2\right)\left(\sin\left(x\right)\right)-\left(x^3\right)\left(\cos\left(x\right)\right)}{\left(\sin\left(x\right)\right)^2}  

c)

(3x2)sin⁡(x)+(x3)cos⁡(x)\left(3x^2\right)\sin\left(x\right)+\left(x^3\right)\cos\left(x\right)  

d)

x3sin⁡(x)−cos⁡(x)x3(sin⁡(x))2\frac{x^3\sin\left(x\right)-\cos\left(x\right)x^3}{\left(\sin\left(x\right)\right)^2}  

91.

If

f(x)=2xf\left(x\right)=2^x  , then ...

a)

f′(x)=2xf'\left(x\right)=2^x  

b)

f′(x)=ln⁡(2)⋅2xf'\left(x\right)=\ln\left(2\right)\cdot2^x  

c)

f′(x)=e2xf'\left(x\right)=e^{2x}  

d)

f′(x)=exln⁡(2)f'\left(x\right)=\frac{e^x}{\ln\left(2\right)}  

92.

If

f(x)=4xf\left(x\right)=4^x  , then ...

a)

f′(x)=4xf'\left(x\right)=4^x  

b)

f′(x)=ln⁡(4)⋅4xf'\left(x\right)=\ln\left(4\right)\cdot4^x  

c)

f′(x)=e4xf'\left(x\right)=e^{4x}  

d)

f′(x)=exln⁡(4)f'\left(x\right)=\frac{e^x}{\ln\left(4\right)}  

93.

If

f(x)=log⁡2(x)f\left(x\right)=\log_2\left(x\right)  , then ...

a)

f′(x)=1xln⁡(2)f'\left(x\right)=\frac{1}{x\ln\left(2\right)}  

b)

f′(x)=ln⁡(2)⋅2xf'\left(x\right)=\ln\left(2\right)\cdot2^x  

c)

f′(x)=12xf'\left(x\right)=\frac{1}{2x}  

d)

f′(x)=2xf'\left(x\right)=\frac{2}{x}  

94.

∫x74 \int_{ }^{ }\frac{x^7}{4\ }

a)

x832+C\frac{x^8}{32}+C

b)

32x6+C\frac{3}{2}x^6+C

c)

28x6+C28x^6+C

d)

32x8+C32x^8+C

95.
a)
b)
c)
d)
96.
a)
b)
c)
d)
97.
a)
b)
c)
d)
98.
a)

3-x2

b)

Limit to infinity

c)

Substitute upper bound into x, multiply by derivative of the upper bound

d)

Take antiderivative, evaluate integral

99.
a)

Substitute in upper bound, multiply by derivative of the upper bound

b)

Take the anti-derivative, evaluate

c)

x2-a

d)

Limit to infinity

100.
a)

Take the derivative

b)

graph the function

c)

Set up to coordinate points, f and f-1. Set point equal to a, solve for x. Find f'(x). Take reciprical - 1/m

d)

Integrate

101.

Separate the variables

a)
b)
c)
d)
102.

Separate the variables

a)
b)
c)
d)
103.

Separate the variables

a)
b)
c)
d)
104.

Separate the variables

a)
b)
c)
d)
105.

Separate the variables

a)
b)
c)
d)
106.

Separate the variables

a)
b)
c)
d)
107.

Separate the variables

a)
b)
c)
d)
108.

Separate the variables

a)
b)
c)
d)
109.

Separate the variables

a)
b)
c)
d)
110.
a)
b)
c)
d)
111.
a)
b)
c)
d)
112.
a)
b)
c)
d)
113.
a)
b)
c)
d)
114.
a)
b)
c)
d)
115.
a)
b)
c)
d)
116.
a)
b)
c)
d)
117.
a)
b)
c)
d)
118.
a)
b)
c)
d)
119.
a)
b)
c)
d)
120.
a)
b)
c)
d)
121.
a)
b)
c)
d)
122.
a)
b)
c)
d)
123.
a)
b)
c)
d)
124.
a)
b)
c)
d)
125.

If you're supposed to find the Average Value of f(x)f\left(x\right)  , then the units of the average value will be...

a)

the same as the unit for f(x)f\left(x\right)  

b)

the units of the ∫f(x)\int_{ }f\left(x\right)  

c)

the units of the derivative of f(x)f\left(x\right)  

126.

Average value is...

a)

1b−a∫abf(x)dx\frac{1}{b-a}\int_a^bf\left(x\right)dx  

b)

f(b)−f(a)b−a\frac{f\left(b\right)-f\left(a\right)}{b-a}  

c)

∫abf(x)dx\int_a^bf\left(x\right)dx  

d)

y−y1=m(x−x1)y-y_1=m\left(x-x_1\right)  

127.

Average rate of change is...

a)

1b−a∫abf(x)dx\frac{1}{b-a}\int_a^bf\left(x\right)dx  

b)

f(b)−f(a)b−a\frac{f\left(b\right)-f\left(a\right)}{b-a}  

c)

∫abf(x)dx\int_a^bf\left(x\right)dx  

d)

y−y1=m(x−x1)y-y_1=m\left(x-x_1\right)  

128.

∫f′(2x)dx\int_{ }^{ }f'\left(2x\right)dx  

a)

12f(2x)\frac{1}{2}f\left(2x\right)  

b)

2f′′(2x)2f''\left(2x\right)  

c)

2f(2x)2f\left(2x\right)  

d)

12f′′(2x)\frac{1}{2}f''\left(2x\right)  

129.

∫f′(12x)dx\int_{ }^{ }f'\left(\frac{1}{2}x\right)dx  

a)

12f(12x)\frac{1}{2}f\left(\frac{1}{2}x\right)  

b)

2f′′(12x)2f''\left(\frac{1}{2}x\right)  

c)

2f(12x)2f\left(\frac{1}{2}x\right)  

d)

12f′′(12x)\frac{1}{2}f''\left(\frac{1}{2}x\right)  

130.

If R(x) is an increasing function, then a Left Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

131.

If R(x) is a decreasing function, then a Left Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

132.

If R(x) is an increasing function, then a Right Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

133.

If R(x) is a decreasing function, then a Right Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

134.

If R(x) is an increasing concave up function, then a Trapezoidal Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

135.

If R(x) is an increasing concave down function, then a Trapezoidal Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

136.

Find the area of the region

a)
b)
c)
d)
137.

Find the area of the region

a)
b)
c)
d)
138.

Find the between the two curves

a)
b)
c)
d)
139.

Find the volume of the solid formed when the region R is rotated about the line y=k

a)
b)
c)
d)
140.

Find the volume of the solid formed when the region R is rotated about the line x=k

a)
b)
c)
d)
141.

Find the volume of the solid formed when cross sections perpendicular to the x axis are squares

a)
b)
c)
d)
142.

Find the volume of the solid formed when cross sections perpendicular to the x axis are isosceles triangles

a)
b)
c)
d)
143.

Find the volume of the solid formed when cross sections perpendicular to the x axis are semi-circles

a)
b)
c)
d)
144.

Find the volume of the solid formed when cross sections perpendicular to the y axis are semi-circles

a)
b)
c)
d)
145.

Find the volume of the solid formed by cross sections perpendicular to the x axis that are rectangles with a height three times the base.

a)
b)
146.

Find the volume of the solid formed when the region is rotated about the line y=8y=8  

a)

π∫08((8−f(x))2−(8−g(x))2)dx\pi\int_0^8\left(\left(8-f\left(x\right)\right)^2-\left(8-g\left(x\right)\right)^2\right)dx

b)

π∫08((8−g(x))2−(8−f(x))2)dx\pi\int_0^8\left(\left(8-g\left(x\right)\right)^2-\left(8-f\left(x\right)\right)^2\right)dx

c)

π∫06((8−g(y))2−(8−f(y))2)dy\pi\int_0^6\left(\left(8-g\left(y\right)\right)^2-\left(8-f\left(y\right)\right)^2\right)dy

d)

π∫06((8−f(y))2−(8−g(y))2)dy\pi\int_0^6\left(\left(8-f\left(y\right)\right)^2-\left(8-g\left(y\right)\right)^2\right)dy

147.

Find the volume of the solid formed when the region is rotated about the line x=8x=8  

a)

π∫08((8−f(x))2−(8−g(x))2)dx\pi\int_0^8\left(\left(8-f\left(x\right)\right)^2-\left(8-g\left(x\right)\right)^2\right)dx

b)

π∫08((8−g(x))2−(8−f(x))2)dx\pi\int_0^8\left(\left(8-g\left(x\right)\right)^2-\left(8-f\left(x\right)\right)^2\right)dx

c)

π∫06((8−g(y))2−(8−f(y))2)dy\pi\int_0^6\left(\left(8-g\left(y\right)\right)^2-\left(8-f\left(y\right)\right)^2\right)dy

d)

π∫06((8−f(y))2−(8−g(y))2)dy\pi\int_0^6\left(\left(8-f\left(y\right)\right)^2-\left(8-g\left(y\right)\right)^2\right)dy

148.

Find the volume of the solid formed when the region is rotated about the line y=−1y=-1  

a)

π∫08((f(x)−(−1))2−(g(x)−(−1))2)dx\pi\int_0^8\left(\left(f\left(x\right)-\left(-1\right)\right)^2-\left(g\left(x\right)-\left(-1\right)\right)^2\right)dx

b)

π∫08((g(x)−(−1))2−(f(x)−(−1))2)dx\pi\int_0^8\left(\left(g\left(x\right)-\left(-1\right)\right)^2-\left(f\left(x\right)-\left(-1\right)\right)^2\right)dx

c)

π∫06((−1−g(y))2−(−1−f(y))2)dy\pi\int_0^6\left(\left(-1-g\left(y\right)\right)^2-\left(-1-f\left(y\right)\right)^2\right)dy

d)

π∫06((−1−f(y))2−(−1−g(y))2)dy\pi\int_0^6\left(\left(-1-f\left(y\right)\right)^2-\left(-1-g\left(y\right)\right)^2\right)dy

149.

Find the volume of the solid formed when the region is rotated about the line x=−1x=-1  

a)

π∫08((f(x)−(−1))2−(g(x)−(−1))2)dx\pi\int_0^8\left(\left(f\left(x\right)-\left(-1\right)\right)^2-\left(g\left(x\right)-\left(-1\right)\right)^2\right)dx

b)

π∫08((g(x)−(−1))2−(f(x)−(−1))2)dx\pi\int_0^8\left(\left(g\left(x\right)-\left(-1\right)\right)^2-\left(f\left(x\right)-\left(-1\right)\right)^2\right)dx

c)

π∫06((g(y)−(−1))2−(f(y)−(−1))2)dy\pi\int_0^6\left(\left(g\left(y\right)-\left(-1\right)\right)^2-\left(f\left(y\right)-\left(-1\right)\right)^2\right)dy

d)

π∫06((f(y)−(−1))2−(g(y)−(−1))2)dy\pi\int_0^6\left(\left(f\left(y\right)-\left(-1\right)\right)^2-\left(g\left(y\right)-\left(-1\right)\right)^2\right)dy

150.

Find the volume of the solid formed when the region is rotated about the x−axisx-axis  

a)

π∫08((f(x))2−(g(x))2)dx\pi\int_0^8\left(\left(f\left(x\right)\right)^2-\left(g\left(x\right)\right)^2\right)dx

b)

π∫06((g(y))2−(f(y))2)dy\pi\int_0^6\left(\left(g\left(y\right)\right)^2-\left(f\left(y\right)\right)^2\right)dy

c)

π∫06((f(y))2−(g(y))2)dy\pi\int_0^6\left(\left(f\left(y\right)\right)^2-\left(g\left(y\right)\right)^2\right)dy

d)

π∫08((g(x))2−(f(x))2)dx\pi\int_0^8\left(\left(g\left(x\right)\right)^2-\left(f\left(x\right)\right)^2\right)dx

151.

Find the volume of the solid formed when the region is rotated about the y−axisy-axis  

a)

π∫08((f(x))2−(g(x))2)dx\pi\int_0^8\left(\left(f\left(x\right)\right)^2-\left(g\left(x\right)\right)^2\right)dx

b)

π∫06((g(y))2−(f(y))2)dy\pi\int_0^6\left(\left(g\left(y\right)\right)^2-\left(f\left(y\right)\right)^2\right)dy

c)

π∫06((f(y))2−(g(y))2)dy\pi\int_0^6\left(\left(f\left(y\right)\right)^2-\left(g\left(y\right)\right)^2\right)dy

d)

π∫08((g(x))2−(f(x))2)dx\pi\int_0^8\left(\left(g\left(x\right)\right)^2-\left(f\left(x\right)\right)^2\right)dx

152.

Find the volume of the solid formed when cross sections perpendicular to the x axis are rectangles with height 5 times its base

a)
b)
c)
d)
153.

Why do we need implicit differentation?

a)

Because the x and y's are on the same side of the equation

b)

Because it's fun

c)

Because we're supposed to learn it

154.

Find the derivative of  2y2y  

a)

y′y'  

b)

11  

c)

2yy′2yy'  

d)

2y′2y'  

155.

Find the derivative of  xyxy  

a)

(1)(y′)+(x)(y)\left(1\right)\left(y'\right)+\left(x\right)\left(y\right)  

b)

(1)(y)+(x)(y′)\left(1\right)\left(y\right)+\left(x\right)\left(y'\right)  

c)

(1)(y′)\left(1\right)\left(y'\right)  

d)

(x)(y′)+(x)(y)\left(x\right)\left(y'\right)+\left(x\right)\left(y\right)  

156.

Find the derivative of x2−xyx^2-xy  


a)

2x−[(1)(y)+(x)(y′)]2x-\left[\left(1\right)\left(y\right)+\left(x\right)\left(y'\right)\right]  

b)

2x−(1)(y)+(x)(y′)2x-\left(1\right)\left(y\right)+\left(x\right)\left(y'\right)  

c)

2x−[(x)(y)+(1)(y′)]2x-\left[\left(x\right)\left(y\right)+\left(1\right)\left(y'\right)\right]  

d)

2x−(1)(y′)2x-\left(1\right)\left(y'\right)  

157.

When you see an  xyxy  or  2x2y2x^2y  or  3xy23xy^2   you need to remember

a)

The product rule!

b)

The quotient rule!

c)

Write a lot!

158.

The derivative of x3+y3x^3+y^3  is


a)

3x2+3y2y′3x^2+3y^2y'  

b)

(3x2)(y3)+(x3)(3y2y′)\left(3x^2\right)\left(y^3\right)+\left(x^3\right)\left(3y^2y'\right)  

c)

3x2+3y23x^2+3y^2  

d)

x3+3y2y′x^3+3y^2y'  

159.

If  x2+2xy=4x^2+2xy=4  , then the first step to finding  dydx\frac{dy}{dx}  is

a)

2x+(2)(y)+(2x)(dydx)=02x+\left(2\right)\left(y\right)+\left(2x\right)\left(\frac{dy}{dx}\right)=0  

b)

2x+(2)(y)+(2x)(1)=02x+\left(2\right)\left(y\right)+\left(2x\right)\left(1\right)=0  

c)

2x+2y dydx=02x+2y\ \frac{dy}{dx}=0  

d)

2x dydx+(2)(y)+(2x)(dydx)=02x\ \frac{dy}{dx}+\left(2\right)\left(y\right)+\left(2x\right)\left(\frac{dy}{dx}\right)=0  

160.

What is the first step of the derivative

sin⁡(xy)=y2 \sin\left(xy\right)=y^{2\ }

a)

cos⁡(xy)((1)(y)+(x)(y′))=2y⋅y′\cos\left(xy\right)\left(\left(1\right)\left(y\right)+\left(x\right)\left(y'\right)\right)=2y\cdot y'

b)

cos⁡(xy)=2y⋅y′\cos\left(xy\right)=2y\cdot y'

c)

sin⁡(xy)((1)(y)+(x)(y′))=2y⋅y′\sin\left(xy\right)\left(\left(1\right)\left(y\right)+\left(x\right)\left(y'\right)\right)=2y\cdot y'

d)

cos⁡((1)((y)+(x)(y′)))=2y⋅y′\cos\left(\left(1\right)\left(\left(y\right)+\left(x\right)\left(y'\right)\right)\right)=2y\cdot y'

161.

What is the first step of the derivative of

ey+y13=2xe^y+y^{\frac{1}{3}}=2^x

a)

ey⋅y′+13y−23⋅y′=2x⋅ln⁡(2)e^y\cdot y'+\frac{1}{3}y^{-\frac{2}{3}}\cdot y'=2^x\cdot\ln\left(2\right)

b)

ey+13y−23=2x⋅ln⁡(2)e^y+\frac{1}{3}y^{-\frac{2}{3}}=2^x\cdot\ln\left(2\right)

c)

ey⋅y′+y13=2x e^y\cdot y'+y^{\frac{1}{3}}=2^{x\ }

162.

Find the distance the particle travels on [a,b]

a)
b)
c)
d)
163.

Find the particle's position at

t=5t=5   given that  x(1)=2x\left(1\right)=2  

a)
b)
c)
d)
164.

Find the particle's displacement on [a,b]

a)
b)
c)
d)
165.
a)

Distance

b)

Displacement

c)

Position

d)

Acceleration

166.
a)

Distance

b)

Displacement

c)

Position

d)

Acceleration

167.
a)

Distance

b)

Displacement

c)

Position

d)

Acceleration

168.

Find the average velocity on [a,b]

a)
b)
c)
d)
169.

Average rate of change

a)
b)
170.

Average Value

a)
b)
171.
a)

Average rate of change

b)

Average value

172.
a)

Average rate of change

b)

Average value

173.
a)
b)
c)
d)
174.

If the velocity and acceleration of a particle have the SAME SIGN, then the particle is...

a)

Speeding Up

b)

Slowing Down

c)

Neither

175.

If the velocity and acceleration of a particle have OPPOSITE SIGNS, then the particle is...

a)

Speeding Up

b)

Slowing Down

c)

Neither

176.

To determine if a particle is speeding up or slowing down at time  rr   , the first thing you need to do is

a)

Find

v(r)v\left(r\right)   and   a(r)a\left(r\right)  

b)

Compare the signs to determine if they are the same or opposite

c)

Make a sign chart for  v(t)v\left(t\right)  

d)

Make a sign chart for  a(t)a\left(t\right)  

177.

If

v(r)=+v\left(r\right)=+  and  a(r)=+a\left(r\right)=+  , then the particle is 

a)

Speeding Up

b)

Slowing Down

c)

Neither

178.

If

v(r)=+v\left(r\right)=+  and  a(r)=−a\left(r\right)=-  , then the particle is 

a)

Speeding Up

b)

Slowing Down

c)

Neither

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