Free Printable BC Calculus Memorization

1.

$\ln1$

a)

$0$

b)

$1$

c)

$e$

d)

DNE

2.

$\ln\ e$

a)

1

b)

0

c)

e

d)

DNE

3.

$e\approx$

a)

3.142

b)

2.718

c)

1.414

d)

1.732

4.

Area of a Trapezoid

a)

$A=\frac{bh}{2}$

b)

$A=\frac{\left(b_1+b_2\right)h}{2}$

c)

$A=\frac{\left(b_1+b_2\right)2}{h}$

d)

$A=\frac{\left(b_1+b_2\right)}{2}$

5.

$\frac{k}{0}$

a)

Undefined

b)

Indeterminate form

c)

0

6.

$\frac{0}{k}$

a)

Undefined

b)

Indeterminate form

c)

0

7.

Rewrite:

$\sqrt[b]{x^a}$

a)

$x^{\frac{a}{b}}$

b)

$x^{\frac{b}{a}}$

c)

$x^{-\frac{a}{b}}$

d)

$x^{-\frac{b}{a}}$

8.

$\cos\ 0$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

9.

$\cos\ \pi$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

10.

$\sin\ \pi$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

11.

$\cos\ \frac{\pi}{2}$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

12.

$\cos\ \frac{3\pi}{2}$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

13.

$\sin\ \frac{\pi}{2}$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

14.

$\sin\ \frac{3\pi}{2}$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

15.

$\sin\ 0$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

16.

$\sin\ 2\pi$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

17.

$\cos\ 2\pi$

a)

$0$

b)

$1$

c)

$-1$

d)

$\frac{\sqrt[]{2}}{2}$

18.

$\cos\ \frac{\pi}{6}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

19.

$\sin\ \frac{\pi}{6}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

20.

$\sin\ \frac{\pi}{4}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

21.

$\cos\ \frac{\pi}{4}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

22.

$\cos\ \frac{\pi}{3}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

23.

$\sin\ \frac{\pi}{3}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

24.

$\sec\ \theta$

a)

$\frac{1}{\sin\ \theta}$

b)

$\frac{1}{\cos\ \theta}$

c)

$\frac{\sin\ \theta}{\cos\ \theta}$

d)

$\frac{\cos\ \theta}{\sin\ \theta}$

25.

$\csc\ \theta$

a)

$\frac{1}{\sin\ \theta}$

b)

$\frac{1}{\cos\ \theta}$

c)

$\frac{\sin\ \theta}{\cos\ \theta}$

d)

$\frac{\cos\ \theta}{\sin\ \theta}$

26.

$\tan\ \theta$

a)

$\frac{1}{\sin\ \theta}$

b)

$\frac{1}{\cos\ \theta}$

c)

$\frac{\sin\ \theta}{\cos\ \theta}$

d)

$\frac{\cos\ \theta}{\sin\ \theta}$

27.

$\lim_{x\rightarrow a}f\left(x\right)\$ exists

a)

Plug in a

b)

$\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)$

c)

$\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

d)

$f\left(a\right)$ exists

28.

Condition for IVT

a)

$f\left(x\right)$ is continuous on $\left[a,\ b\right]$

b)

$f\left(x\right)$ is differentiable on $\left(a,\ b\right)$

c)

$\lim_{x\rightarrow a}f\left(x\right)\$ exists

d)

$\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)$

29.

Analysis for IVT

a)

There is a c, a < c < b, such that

$f\left(a\right)<f\left(c\right)<f\left(b\right)$

b)

There is a c, a < c < b, such that

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

c)

$\lim_{x\rightarrow a}f\left(x\right)$ exists

$f\left(a\right)$ exists
$\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

d)

$\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)$

30.

Definition of Continuity

a)

There is a c, a < c < b, such that

$f\left(a\right)<f\left(c\right)<f\left(b\right)$

b)

There is a c, a < c < b, such that

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

c)

$\lim_{x\rightarrow a}f\left(x\right)$ exists

$f\left(a\right)$ exists
$\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

d)

$\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)$

31.

Average Rate of Change

a)

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

b)

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

c)

$\frac{f\left(b\right)+f\left(a\right)}{2}$

d)

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

32.

Instantaneous Rate of Change

a)

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

b)

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

c)

Integral

d)

Derivative

33.

Derivative Fails to Exist

a)

cusp, sharp turn
discontinuity
- vertical tangent line

b)

smooth curve

continuous

horizontal tangent line

c)

cusp, sharp turn

discontinuity

horizontal tangent line

d)

smooth curve

continuous

vertical tangent line

34.

Vertical Tangent Line

a)

Derivative is undefined

b)

$f'\left(a\right)=0$

c)

Derivative exists

d)

Limit exists

35.

Horizontal Tangent Line

a)

Derivative is undefined

b)

$f'\left(a\right)=0$

c)

Derivative exists

d)

Limit exists

36.

Critical Numbers

a)

Numbers that tell you what you are doing wrong

b)

$f'\left(a\right)=0$

or undefined

c)

$f\left(a\right)=0$

or undefined

d)

$f'\left(a\right)=0$

37.

$f$ is increasing

a)

$f'>0$

b)

$f'<0$

c)

$f''>0$

d)

$f''<0$

38.

$f$ is decreasing

a)

$f'>0$

b)

$f'<0$

c)

$f''>0$

d)

$f''<0$

39.

$f$ is concave up

a)

$f'$ increasing

$f''<0$

b)

$f'$ decreasing

$f''>0$

c)

$f'$ increasing

$f''>0$

d)

$f'$ decreasing

$f''<0$

40.

$f$ is concave down

a)

$f'$ increasing

$f''<0$

b)

$f'$ decreasing

$f''>0$

c)

$f'$ increasing

$f''>0$

d)

$f'$ decreasing

$f''<0$

41.

$f$ has a relative maximum

a)

$f'=0\ or\ undef.$

and changes

$+\ to\ -$

b)

$f'=0\ or\ undef.$

and changes

$-\ to\ +$

c)

$f''=0\ or\ undef.$

and changes

$+\ to\ -$

d)

$f''=0\ or\ undef.$

and changes

$-\ to\ +$

42.

$f$ has a relative minimum

a)

$f'=0\ or\ undef.$

and changes

$+\ to\ -$

b)

$f'=0\ or\ undef.$

and changes

$-\ to\ +$

c)

$f''=0\ or\ undef.$

and changes

$+\ to\ -$

d)

$f''=0\ or\ undef.$

and changes

$-\ to\ +$

43.

$f$ has an inflection point

a)

$f'$ has a

relative max or min

b)

$f''$ has a

relative max or min

c)

$f''=0\ or\ undef.$

and changes

signs

d)

$f'=0\ or\ undef.$

and changes

signs

44.

$\frac{d}{dx}\tan\ x$

a)

$\sec^2x$

b)

$-\sec^2x$

c)

$\sec\ x\ \cdot\tan\ x$

d)

$\csc\ x\ \cdot\tan\ x$

45.

$\frac{d}{dx}\cot\ x$

a)

$\csc^2x$

b)

$-\csc^2x$

c)

$\sec\ x\ \cdot\cot\ x$

d)

$-\csc\ x\ \cdot\cot\ x$

46.

$\frac{d}{dx}\sec\ x$

a)

$\tan^2x$

b)

$\sec\ x\cdot\cot\ x$

c)

$\sec\ x\ \cdot\tan\ x$

d)

$\csc\ x\ \cdot\tan\ x$

47.

$\frac{d}{dx}\csc\ x$

a)

$\cot^2x$

b)

$-\csc\ x\cdot\cot\ x$

c)

$\csc\ x\ \cdot\tan\ x$

d)

$-\csc\ x\ \cdot\tan\ x$

48.

$\frac{d}{dx}\csc\ x$

a)

$\cot^2x$

b)

$-\csc\ x\cdot\cot\ x$

c)

$\csc\ x\ \cdot\tan\ x$

d)

$-\csc\ x\ \cdot\tan\ x$

49.

$\int_a^bf'\left(x\right)dx$

a)

$f\left(b\right)-f\left(a\right)$

b)

$f'\left(b\right)-f'\left(a\right)$

c)

$f\left(a\right)-f\left(b\right)$

d)

$f'\left(a\right)-f'\left(b\right)$

50.

Average Value

a)

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

b)

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

c)

$\frac{f\left(b\right)+f\left(a\right)}{2}$

d)

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

51.

Displacement

a)

$\int_a^bv\left(t\right)dt$

b)

$\int_a^ba\left(t\right)dt\approx$

c)

$\int_a^b\left|v\left(t\right)\right|dt$

d)

$x\left(a\right)+\int_a^bv\left(t\right)dt$

52.

Total Distance Traveled

a)

$\int_{ }^{ }v\left(t\right)dt$

b)

$\int_{ }^{ }a\left(t\right)dt$

c)

$\int_a^b\left|v\left(t\right)\right|dt$

d)

$x\left(a\right)+\int_a^bv\left(t\right)dt$

53.

$\int_{ }^{ }\ \frac{1}{x}\ dx$

a)

$\frac{1}{x}+C$

b)

$\ln\ x+C$

c)

$\ln\left|x\right|+C$

54.

$\int_{ }^{ }\ \sec x\tan x\ dx$

a)

$\sec\ x+C$

b)

$\tan\ x+C$

c)

$-\sec\ x+C$

d)

$\tan^2x+C$

55.

$\int_{ }^{ }\ \sec^2x\ dx$

a)

$\sec\ x+C$

b)

$\tan\ x+C$

c)

$\sec\ x\tan x+C$

d)

$\tan^2x+C$

56.

$\int_{ }^{ }\ \csc x\cot x\ dx$

a)

$-\csc\ x+C$

b)

$-\cot\ x+C$

c)

$\csc\ x+C$

d)

$\cot^2x+C$

57.

$\int_{ }^{ }\ \csc^2x\ dx$

a)

$-\csc\ x+C$

b)

$-\cot\ x+C$

c)

$\csc\ x\cot x+C$

d)

$\cot^2x+C$

58.

$\frac{\text{d}}{\text{d}x}\int_a^xf\left(t\right)dt$

a)

$f\left(x\right)$

b)

$f'\left(x\right)$

c)

$f\left(a\right)$

d)

$0$

59.

$\frac{\text{d}}{\text{d}x}\int_a^{g\left(x\right)}f\left(t\right)dt$

a)

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

b)

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

c)

$f\left(g\left(x\right)\right)$

d)

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

60.

$\int_{ }^{ }\text{}a^xdx$

a)

$\int_{ }^{ }\frac{a^x}{\ln a}+C$

b)

$\frac{a^x}{\ln a}+C$

c)

$\frac{a^x}{\ln a}$

d)

$a^x+C$

61.

$\int_{ }^{ }\frac{1}{\sqrt{a^2-u^2}\text{}}du$

a)

$\sin^{-1}\frac{u}{a}+C$

b)

$\frac{1}{a}\tan^{-1}\frac{u}{a}+C$

c)

$\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C$

62.

$\int\frac{1}{u^2+a^2}du$

a)

$\sin^{-1}\frac{u}{a}+C$

b)

$\frac{1}{a}\tan^{-1}\frac{u}{a}+C$

c)

$\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C$

63.

$\int_{ }^{ }\frac{1}{u\sqrt{u^2-a^2}}du$

a)

$\sin^{-1}\frac{u}{a}+C$

b)

$\frac{1}{a}\tan^{-1}\frac{u}{a}+C$

c)

$\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C$

64.

Exponential Growth:

a)

$E\left(x\right)=Ce^{kt}$

b)

$E\left(x\right)=Ce^{rkt}$

c)

$E\left(x\right)=e^{kt}$

d)

$E\left(x\right)=e^{kt}+C$

65.

Area between two curves:

a)

$\int_a^bf\left(x\right)-g\left(x\right)dx$

b)

$\int_a^bf\left(x\right)+g\left(x\right)dx$

c)

$\int_a^bf\left(x\right)g\left(x\right)dx$

d)

$\int_a^bf\left(x\right)dx$

66.

$\int_a^af\left(x\right)dx$

a)

0

b)

1

c)

-1

d)

f(a)

67.

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)

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

68.

The intermediate value theorem (IVT) is primarily concerned with which of the following?

a)

y-values

b)

first derivative values

c)

second derivative values

d)

x-values

69.

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)

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

70.

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\ \$

71.

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\ \$

72.

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\ \$

73.

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\ \$

74.

What does the Extreme Value Theorem remind us to do?

a)

Check the endpoints! They might be the max/min.

b)

Check the inflection points! They might be the max/min.

c)

Check the endpoints! They give the secant slope.

d)

Check the inflection points! They are when the derivative is 0.

75.

What is the formula for areaof a circle given the radius?

a)

A = πr

b)

A = 2πr

c)

A = πd

d)

A = πr²

76.

According to the quotient rule: $\frac{\text{d}}{\text{d}x}\frac{f\left(x\right)}{g\left(x\right)}$ =

a)

$\frac{f'\left(x\right)g\left(x\right)-g'\left(x\right)f\left(x\right)}{\left(g\left(x\right)\right)^2}$

b)

$\frac{g'\left(x\right)f\left(x\right)-f'\left(x\right)g\left(x\right)}{\left(g\left(x\right)\right)^2}$

c)

$\frac{f'\left(x\right)g\left(x\right)+g'\left(x\right)f\left(x\right)}{\left(g\left(x\right)\right)^2}$

d)

$\frac{f'\left(x\right)}{g'\left(x\right)}$

77.

In general, what is the formula for the derivative of an exponential function?

$\frac{d}{dx}a^x$ =

a)

$x\cdot a^{x-1}$

b)

$a^x\ln a$

c)

$a^x$

d)

$a^x\ln e$

78.

In general, what is the derivative for a logarithmic function?

$\frac{\text{d}}{\text{d}x}\log_ax=$

a)

$\frac{1}{x\ln a}$

b)

$\frac{1}{x\ln e}$

c)

$\frac{1}{x}$

d)

$\frac{1}{a\ln x}$

79.

a)

speed

b)

acceleration

c)

displacement

d)

total distance

80.

$V=\int_a^b\left(top-bottom\right)^2dx$

a)

Square cross section volume

b)

Equilateral triangle cross section volume

c)

Semi circle cross section volume

d)

Isosceles right triangle cross section volume

81.

$V=\frac{\pi}{8}\int_a^b\left(top-bottom\right)^2dx$

a)

Square cross section volume

b)

Equilateral triangle cross section volume

c)

Semi circle cross section volume

d)

Isosceles right triangle cross section volume

82.

$V=\frac{\sqrt[]{3}}{4}\int_a^b\left(top-bottom\right)^2dx$

a)

Square cross section volume

b)

Equilateral triangle cross section volume

c)

Semi circle cross section volume

d)

Isosceles right triangle cross section volume

83.

$V=\frac{1}{2}\int_a^b\left(top-bottom\right)^2dx$

a)

Isosceles right triangle with hypotenuse as base cross section volume

b)

Equilateral triangle cross section volume

c)

Semi circle cross section volume

d)

Isosceles right triangle with leg as base cross section volume

84.

$V=\frac{1}{4}\int_a^b\left(top-bottom\right)^2dx$

a)

Isosceles right triangle with hypotenuse as base cross section volume

b)

Equilateral triangle cross section volume

c)

Semi circle cross section volume

d)

Isosceles right triangle with leg as base cross section volume

85.

Please select the correct solution
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

86.

Move the equations to the correct spots.

a)

\frac{dy}{dt}=ky

b)

y=Ce^{kt}

c)

\frac{dP}{dt}=kP\left(1-\frac{P}{L}\right)

d)

P=\frac{L}{1+Ae^{-kt}}

1

2

3

4

1)

2)

3)

4)

87.

Arc length from x=a to x=b

a)

$\int_a^b\left(1+\left(f'\left(x\right)\right)^2\right)dx$

b)

$\int_a^b\left(1+f'\left(x\right)\right)dx$

c)

$\int_a^b\left(f'\left(x\right)\right)^2dx$

d)

$\int_a^b\left(1+\left(f\left(x\right)\right)^2\right)dx$

88.

Arc length for parametric and vector equations

a)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}dt$

b)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^{ }+\left(\frac{dy}{dt}\right)^{ }}dt$

c)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^2-\left(\frac{dy}{dt}\right)^2}dt$

d)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^{ }-\left(\frac{dy}{dt}\right)^{ }}dt$

89.

Total distance for vectors

a)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}dt$

b)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^{ }+\left(\frac{dy}{dt}\right)^{ }}dt$

c)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^2-\left(\frac{dy}{dt}\right)^2}dt$

d)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^{ }-\left(\frac{dy}{dt}\right)^{ }}dt$

90.

Speed

$\left|v\left(t\right)\right|$

a)

$\sqrt[]{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}$

b)

$\sqrt[]{\left(\frac{dx}{dt}\right)^{ }+\left(\frac{dy}{dt}\right)^{ }}$

c)

$\int_{t_1}^{t_2}\sqrt[]{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}dt$

d)

$\sqrt[]{\left(\frac{dx}{dt}\right)^2-\left(\frac{dy}{dt}\right)^2}$

91.

Match the following

Categorize the following

+ velocity & + acc.

- velocity & + acc.

- velocity & - acc.

+ velocity & - acc.

Speed increasing

Speed decreasing

92.

Polar area

a)

$\frac{1}{2}\int_{\theta_1}^{\theta_2}r^2d\theta$

b)

$\int_{\theta_1}^{\theta_2}r^2d\theta$

c)

$\frac{1}{2}\int_{\theta_1}^{\theta_2}r^{ }d\theta$

d)

$\frac{1}{4}\int_{\theta_1}^{\theta_2}r^2d\theta$

93.

Parametric 1st Derivative

$\frac{dy}{dx}=$

a)

$\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

b)

$\frac{\frac{dx}{dt}}{\frac{dy}{dt}}$

94.

Parametric 2nd Derivative

$\frac{d^2y}{dx^2}=$

a)

$\frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dx}{dt}}$

b)

$\frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dy}{dt}}$

c)

$\frac{d}{dt}\left(\frac{dy}{dx}\right)$

d)

$\frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dx}{dt}\cdot\frac{dy}{dt}}$

95.

Polar conversion:

$x=$

a)

$r\cos\theta$

b)

$r\sin\theta$

c)

$r\tan\theta$

96.

Polar conversion:

$y=$

a)

$r\cos\theta$

b)

$r\sin\theta$

c)

$r\tan\theta$

97.

Using the nth term test

If $\lim_{n\rightarrow\infty}a_n=0$ then the series

a)

converges

b)

diverges

c)

the test is inconclusive - pick a different one

98.

Using the nth term test

If $\lim_{n\rightarrow\infty}a_n\ne0$ then the series

a)

converges

b)

diverges

c)

the test is inconclusive - pick a different one

99.

A p-series where $p>1$ then the series will...

a)

converge

b)

diverge

c)

the test is inconclusive - pick a different one

100.

A p-series where $0<p\le1$ then the series will...

a)

converge

b)

diverge

c)

the test is inconclusive - pick a different one

101.

The harmonic series

$\sum_{n=1}^{\infty}\frac{1}{n}$

always...

a)

diverges

b)

converges

102.

In a geometric series, if $\left|r\right|\ge1$ then the series will...

a)

diverge

b)

converge

c)

test is inconclusive, pick a different one

103.

In a geometric series, if $\left|r\right|<1$ then the series will...

a)

diverge

b)

converge

c)

test is inconclusive, pick a different one

104.

A convergent geometric series, will converge to...

a)

$\frac{1st\ term}{1-r}$

b)

$\frac{1st\ term}{r-1}$

c)

$\frac{1st\ term}{1+r}$

105.

What are the requirements for the integral test to be applied:

(a) (b) (c)

PUT your answers in ALPHABETICAL ORDER

Choose from the below words

discontinous

differentiable

increasing

negative

continuous

decreasing

positive

106.

If $a_n=f\left(n\right)$ is continuous, positive, and decreasing, and $\int_1^{\infty}f\left(n\right)dn$ converges then $\sum_{n=1}^{\infty}a_n$ will...

a)

converge

b)

diverge

c)

test is inconclusive - pick a different one!

107.

If $a_n=f\left(n\right)$ is continuous, positive, and decreasing, and $\int_1^{\infty}f\left(n\right)dn=\pm\infty$ then $\sum_{n=1}^{\infty}a_n$ will...

a)

converge

b)

diverge

c)

test is inconclusive - pick a different one!

108.

Comparison test:

Let $0<a_n\le b_n$ for all n.

If $\sum_{n=1}^{\infty}b_n$ converges, then $\sum_{n=1}^{\infty}a_n$ (a)

If $\sum_{n=1}^{\infty}a_n$ diverges, then $\sum_{n=1}^{\infty}b_n$ (b)

If $\sum_{n=1}^{\infty}b_n$ diverges, then (c)

If $\sum_{n=1}^{\infty}a_n$ converges, then (d)

Choose from the below words

converges

diverges

$\sum_{n=1}^{\infty}a_n\ is\ unknown$

$\sum_{n=1}^{\infty}b_n\ is\ unknown$

109.

In the limit comparison test, if $\lim_{n\rightarrow\infty}\left(\frac{a_n}{b_n}\right)=a\ finite,\ positive\ number$ then....

a)

$a_n$ and $b_n$ either both converge or both diverge

b)

$a_n$ and $b_n$ both diverge

c)

$a_n$ and $b_n$ both converge

d)

the test is inconclusive - pick a different oen!

110.

For an alternating series, select the TWO requirements in order to prove convergence by the Alternating Series Test. (assume the series is alternating)

a)

$\lim_{n\rightarrow\infty}a_n=0$

b)

$\lim_{n\rightarrow\infty}a_n\ne0$

c)

$\frac{a_{\left(n+1\right)}}{a_n}<1$

(series is decreasing)

d)

$\frac{a_{\left(n+1\right)}}{a_n}>1$

(series is increasing)

111.

$\frac{\left(n+1\right)!}{n!}=$

a)

$1$

b)

$n$

c)

$n+1$

d)

$n!$

112.

$\left(n+1\right)!=$

a)

$1$

b)

$n!+1!$

c)

$\left(n+1\right)n!$

d)

$n!$

113.

Based on the Ratio Test for Convergence, if $\sum_{n=1}^{\infty}a_n$ has positive terms and $\lim_{n\rightarrow\infty}\left(\frac{a_{\left(n+1\right)}}{a_n}\right)<1$ then the series...

a)

converges

b)

diverges

c)

test is inconclusive - pick a different one!

114.

Based on the Ratio Test for Convergence, if $\sum_{n=1}^{\infty}a_n$ has positive terms and $\lim_{n\rightarrow\infty}\left(\frac{a_{\left(n+1\right)}}{a_n}\right)>1$ then the series...

a)

converges

b)

diverges

c)

test is inconclusive - pick a different one!

115.

Based on the Ratio Test for Convergence, if $\sum_{n=1}^{\infty}a_n$ has positive terms and $\lim_{n\rightarrow\infty}\left(\frac{a_{\left(n+1\right)}}{a_n}\right)=1$ then the series...

a)

converges

b)

diverges

c)

test is inconclusive - pick a different one!

BC Calculus Memorization

Total questions: 115

Worksheet time: 29hrs 45mins

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