Free Printable AB Calculus Mixed Review

1.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

2.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

3.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

4.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

5.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

6.

a)

Mean value theorem

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

7.

Let f be the function defined by f(x)=4x³-10x+5. Find the equation of the tangent line to the graph of f at the point where x = 1

a)

y+1=2(x-1)

b)

y-1=2(x-1)

c)

y+1=2(x+1)

d)

y+1=-2(x-1)

8.

If g is the inverse function of F and f(2)=3, find the value of g'(3) for F(x)=6x²+2x-1

a)

1/24

b)

1/25

c)

1/26

d)

26

9.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

10.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

11.

What is the derivative of the function $f\left(x\right)=\int_1^{2x}\ \ 6e^x\ dx$

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

12.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

13.

a)

f(a) - f(b)

b)

f(b) - f(a)

c)

f '(b) - f '(a)

d)

f '(a) - f '(b)

14.

a)

position

b)

velocity

c)

acceleration

d)

total distance

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

e)

E

17.

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

18.

The image displays the ______

a)

Limit definition of the first derivative

b)

The bane of my existance

19.

Which of the following does not apply to being a critical value if f is to be defined at x=c?

a)

f '(c)=0

b)

f'(c)=x

c)

f'(c)=1

d)

f'(c) does not exist

20.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

Hint: Use u substitution

a)

A

b)

B

c)

C

d)

D

26.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

27.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

28.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

29.

Integrate $\int\ \frac{1}{^3\sqrt{x}}\ dx$

a)

$\frac{2x^{\frac{3}{2}}}{3}+c$

b)

$\frac{3x^{\frac{2}{3}}}{2}+c$

c)

$\frac{3x^{\frac{2}{3}}}{2}$

d)

$6x^{\frac{3}{2}}+c$

30.

a)

A

b)

B

c)

C

d)

D

31.

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?

I. g has at least one horizontal tangent line.

II. g has at least 2 zeros.

III. For some c in the interval (3, 6), f'(c) = -7/3.

a)

II only

b)

II and III

c)

I and II

d)

I, II, and III

32.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

33.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

a)

2

b)

4

c)

6

d)

8

34.

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t² - 4.
What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

22

d)

44

35.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

a)

2

b)

4

c)

6.5

d)

7

36.

If $f'\left(a\right)=0$ and $f'\left(x\right)$ changes from positive to negative at $x=a$ , then $f\left(x\right)$ has

a)

A relative maximum at x=a

b)

A relative minimum at x=a

c)

No relative extrema at x=a

d)

A vertical tangent line at x=a

37.

Which of the following could be the graph of f ' , the derivative of f ?

a)

b)

c)

d)

e)

38.

On what interval(s) is the function $f\left(x\right)=x^3+6x^2$ concave down?

a)

$\left(-\infty,-4\right)$

b)

$\left(-\infty,-2\right)$

c)

$\left(-2,\infty\right)$

d)

$\left(0,\infty\right)$

39.

What is the derivative of sin(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

40.

What is the derivative?

a)

A

b)

B

c)

C

d)

D

41.

What is the derivative of cos(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

42.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

43.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

44.

f(x)=5x
find f'(x)

a)

5

b)

1

c)

0

d)

5x

45.

y=9
y'=

a)

9

b)

0

c)

1

d)

undefinded

46.

f(x)= 5/x^{2
f'(x) =}

a)

5x

b)

5/2x

c)

5x^-2

d)

-10/x³

47.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

48.

d/dx (sin²x) = ?

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

49.

Find dy/dx for
y = (x² + 1)³

a)

dy/dx = 3(x² + 1)²

b)

dy/dx = 3(2x)²

c)

dy/dx = 3(x² + 1)²(2x)

d)

dy/dx = 2x(x² + 1)²

50.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

51.

Find the derivative of g(x)=(3x-2)/(x²+2)

a)

9x²+2

b)

3(x²+2)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

52.

Find the derivative: h(x)=(3x+2)(5x³+2x)

a)

60x³+30x +12x-4

b)

60x³-30x²+12x-4

c)

45x³+30x²+12x+4

d)

60x³+30x²+12x+4

53.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

54.

The derivative of

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

55.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

56.

Find the derivative. f(x) = -8x^-3 + 5x - e^x

a)

f'(x) = -24x^-4 + 5 - e^x

b)

f'(x) = 24x^-4 + 5 - e^x

c)

f'(x) = 24x^-2 + 5 - e^x

d)

f'(x) = 24x^-4 + 5 - e^x-1

57.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

58.

A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?

a)

57.60

b)

57.88

c)

59.20

d)

67.40

59.

The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere? (The surface area of a sphere is A = 4πr².)

a)

-108π

b)

-72π

c)

-48π

d)

-24π

60.

Which of the following best describes the continuity at x = 0?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

61.

Which of the following best describes the continuity at x = -3?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

62.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

63.

What is the limit?

a)

DNE

b)

6

c)

0

d)

12

64.

$\int_0^{\frac{\pi}{4}}\sin x\ dx+\int_{-\frac{\pi}{4}}^0\cos x\ dx=$

a)

$-\ \sqrt[]{2}$

b)

$-1$

c)

$0$

d)

$1$

65.

Boats $A$ and $B$ leave the same place at the same time. Boat $A$ heads due north at $12\frac{\text{km}}{\text{hr}}$ . Boat $B$ heads due east at $18\frac{\text{km}}{\text{hr}}$ . After $2.5$ hours, how fast is the distance between the boats increasing (in $\frac{\text{km}}{\text{hr}}$ )?

a)

$21.63$

b)

$31.2$

c)

$9.84$

d)

$54.08$

66.

$\lim_{h\rightarrow0}\frac{\tan\left(\frac{\pi}{6}+h\right)-\tan\left(\frac{\pi}{6}\right)}{h}=$

a)

$\frac{\sqrt[]{3}}{3}$

b)

$\frac{4}{3}$

c)

$0$

d)

$\frac{3}{4}$

67.

If $\int_{30}^{100}f\left(x\right)dx=A$ and $\int_{50}^{100}f\left(x\right)dx=B$ , then $\int_{30}^{50}f\left(x\right)dx=$

a)

$A+B$

b)

$A-B$

c)

$B-A$

d)

$20$

68.

The graph of $y=x^3-5x^2+4x+2$ has a local minimum at

a)

$\left(0.46,2.87\right)$

b)

$\left(2.87,-4.06\right)$

c)

$\left(4.06,2.87\right)$

d)

$\left(1.66,-0.59\right)$

69.

The volume generated by revolving about the $y$ -axis the region enclosed by the graphs $y=9-x^2$ and $y=9-3x$ , for $0\le x\le2$ , is

a)

$4\pi$

b)

$8\pi$

c)

$24\pi$

d)

$48\pi$

70.

The average value of the function $f\left(x\right)=\left(\ln x\right)^2$ on the interval $\left[2,4\right]$ is

a)

$1.204$

b)

$2.159$

c)

$2.408$

d)

$8.636$

71.

$\frac{d}{dx}\left(\int_0^{3x}\cos t\ dt\right)=$

a)

$\sin3x$

b)

$-3\sin3x$

c)

$3\sin3x$

d)

$3\cos3x$

72.

Error is defined as the positive difference between an actual value and an approximation. If the definite integral $\int_1^3\left(x^2+1\right)dx$ is approximated by using a trapezoid sum with $4$ trapezoids, the error is

a)

$\frac{7}{3}$

b)

$\frac{1}{12}$

c)

$\frac{65}{6}$

d)

$\frac{97}{3}$

73.

The radius of a sphere is increasing at a rate proportional to itself. If the radius is $4$ initially, and the radius is $10$ after $2$ seconds, what will the radius be after $3$ seconds?

a)

$62.5$

b)

$13$

c)

$15.81$

d)

$16$

74.

Approximate the change in the volume of a sphere when the radius is increased from $10$ to $10.02\ \text{cm}$ .

a)

$4213.973$

b)

$1256.637$

c)

$25.233$

d)

$25.183$

75.

$\int_{ }^{ }\ln2x\ dx=$

a)

$\frac{\ln2x}{x}+C$

b)

$\frac{\ln2x}{2x}+C$

c)

$x\ln2x-x+C$

d)

$2x\ln2x-2x+C$

76.

If the function $f\left(x\right)$ is differentiable, and:

$f\left(x\right)=ax^3-6x$ if $x\le1$ ,

$f\left(x\right)=bx^2+4$ if $x>1$ ,

then $a=$

a)

$1$

b)

$-14$

c)

$-24$

d)

$26$

77.

Two particles leave the origin at the same time and move along the $y$ -axis with their respective positions determined by the functions $y_1=\cos2t$ and $y_2=4\sin t$ for $0<t<6$ . For how many values of $t$ do the particles have the same acceleration?

a)

$0$

b)

$1$

c)

$2$

d)

$3$

78.

Find the distance traveled in the first four seconds for a particle whose velocity is given by $v\left(t\right)=7e^{-t^2}$ where $t$ stands for time in seconds.

a)

$0.976$

b)

$6.204$

c)

$6.359$

d)

$12.72$

79.

$\int_{ }^{ }\tan^6x\sec^2x\ dx=$

a)

$\frac{\tan^7x}{7}+C$

b)

$\frac{\tan^7x}{7}+\frac{\sec^3x}{3}+C$

c)

$\frac{\tan^7x\sec^3x}{21}+C$

d)

$\frac{2}{7}\tan^7x\sec x+C$

80.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

81.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

82.

Find the volume of a solid generated by the graph bounded by y=x² and the line y =9 when it is revolved around the x-axis

a)

456

b)

610.73

c)

194.4

d)

610.726

83.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

84.

Alec consumes beverages at a rate of r(x)=10+.2x²beverages per hour, how many beverages does Alec drink in the first 16 hours?

a)

25.068

b)

433.067

c)

5463.759

d)

Too many, Alec should seek medical attention

85.

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

86.

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

87.

Which of these is the definition of a derivative?

a)

$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

b)

$\lim_{h\rightarrow0}\ \frac{f\left(h\right)-f\left(x\right)}{h}$

c)

$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)+f\left(x\right)}{h}$

d)

$\lim_{h\rightarrow0}\ \frac{f\left(h\right)+f\left(x\right)}{h}$

88.

Which of these sums up the Mean Value Theorem (MVT)?

a)

$f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$f\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$f\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

d)

$f'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

89.

Volume using discs revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

c)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

90.

Volume using discs revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

c)

$\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

91.

Volume using washers revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}R^2-r^2\ dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(R-r\right)^{2\ }dx\ \$

c)

$\int_{x=a}^{x=b}\left(R-r\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}R^{2\ }-r^{2\ }dx\ \$

92.

Volume using washers revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

c)

$\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

93.

a)

A

b)

B

c)

C

d)

D

e)

E

94.

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

95.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

96.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

97.

a)

A

b)

B

c)

C

d)

D

98.

a)

A

b)

B

c)

C

d)

D

99.

Which equation below represents the slope field?

a)

dy/dx = x - 2

b)

dy/dx = 1/2x + 1

c)

dy/dx =1/2 y - 2

d)

dy/dx = y + 2

100.

dy/dx = 4x/y. Suppose y(0)=1
The particular solution is

a)

B

b)

C

c)

D

d)

E

101.

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution. Which of the following statements is true if the particular solution contains (0,-1)

a)

g(x) is increasing and concave up

b)

g(x) is increasing and concave down

c)

g(x) is decreasing and concave up

d)

g(x) is decreasing and concave down

102.

Find the Particular Solution

a)

$y=2+e^{\left(\frac{x^2}{2}+x\right)}$

b)

$y=2e^{\left(\frac{x^2}{2}+x\right)}$

c)

$y=\ln\left|\frac{x^2}{2}+x+1\right|+2$

d)

$y=\ln\left|\frac{x^2}{2}+x+e^2\right|$

103.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

$y=\frac{e^x}{2}+C$

c)

$y=e^x+C$

d)

$0=e^x+C$

104.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=3y$

a)

$y=Ce^{3x}$

b)

$y=3x+C$

c)

$\frac{y^2}{2}=3x+C$

d)

$\ln y=x+C$

105.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

106.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

107.

Find the volume of a solid generated by the graph bounded by y=x² and the line y =9 when it is revolved around the x-axis

a)

456

b)

610.73

c)

194.4

d)

610.726

108.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

109.

Alec consumes beverages at a rate of r(x)=10+.2x²beverages per hour, how many beverages does Alec drink in the first 16 hours?

a)

25.068

b)

433.067

c)

5463.759

d)

Too many, Alec should seek medical attention

110.

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

111.

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

112.

Which of these is the definition of a derivative?

a)

$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

b)

$\lim_{h\rightarrow0}\ \frac{f\left(h\right)-f\left(x\right)}{h}$

c)

$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)+f\left(x\right)}{h}$

d)

$\lim_{h\rightarrow0}\ \frac{f\left(h\right)+f\left(x\right)}{h}$

113.

Which of these sums up the Mean Value Theorem (MVT)?

a)

$f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$f\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$f\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

d)

$f'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

114.

Volume using discs revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

c)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

115.

Volume using discs revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

c)

$\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

116.

Volume using washers revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}R^2-r^2\ dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(R-r\right)^{2\ }dx\ \$

c)

$\int_{x=a}^{x=b}\left(R-r\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}R^{2\ }-r^{2\ }dx\ \$

117.

Volume using washers revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

c)

$\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

118.

a)

A

b)

B

c)

C

d)

D

e)

E

119.

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

120.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

121.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

122.

a)

A

b)

B

c)

C

d)

D

123.

a)

A

b)

B

c)

C

d)

D

124.

Which equation below represents the slope field?

a)

dy/dx = x - 2

b)

dy/dx = 1/2x + 1

c)

dy/dx =1/2 y - 2

d)

dy/dx = y + 2

125.

dy/dx = 4x/y. Suppose y(0)=1
The particular solution is

a)

B

b)

C

c)

D

d)

E

126.

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution. Which of the following statements is true if the particular solution contains (0,-1)

a)

g(x) is increasing and concave up

b)

g(x) is increasing and concave down

c)

g(x) is decreasing and concave up

d)

g(x) is decreasing and concave down

127.

Find the Particular Solution

a)

$y=2+e^{\left(\frac{x^2}{2}+x\right)}$

b)

$y=2e^{\left(\frac{x^2}{2}+x\right)}$

c)

$y=\ln\left|\frac{x^2}{2}+x+1\right|+2$

d)

$y=\ln\left|\frac{x^2}{2}+x+e^2\right|$

128.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

$y=\frac{e^x}{2}+C$

c)

$y=e^x+C$

d)

$0=e^x+C$

129.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=3y$

a)

$y=Ce^{3x}$

b)

$y=3x+C$

c)

$\frac{y^2}{2}=3x+C$

d)

$\ln y=x+C$

130.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

AB Calculus Mixed Review

Total questions: 130

Worksheet time: 11hrs 50mins

Similar Resources on Wayground