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Worksheets

AB Calculus Memorization

Total questions: 86

Worksheet time: 4hrs 18mins

Name
Class
Date
1.

ln⁡1\ln1

a)

00

b)

11

c)

ee

d)

DNE

2.

ln⁡ e\ln\ e

a)

1

b)

0

c)

e

d)

DNE

3.

e≈e\approx

a)

3.142

b)

2.718

c)

1.414

d)

1.732

4.

Area of a Trapezoid

a)

A=bh2A=\frac{bh}{2}

b)

A=(b1+b2)h2A=\frac{\left(b_1+b_2\right)h}{2}

c)

A=(b1+b2)2hA=\frac{\left(b_1+b_2\right)2}{h}

d)

A=(b1+b2)2A=\frac{\left(b_1+b_2\right)}{2}

5.

k0\frac{k}{0}

a)

Undefined

b)

Indeterminate form

c)

0

6.

0k\frac{0}{k}

a)

Undefined

b)

Indeterminate form

c)

0

7.

Rewrite:

xab\sqrt[b]{x^a}

a)

xabx^{\frac{a}{b}}

b)

xbax^{\frac{b}{a}}

c)

x−abx^{-\frac{a}{b}}

d)

x−bax^{-\frac{b}{a}}

8.

cos⁡ 0\cos\ 0

a)

00

b)

11

c)

−1-1

d)

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

9.

cos⁡ π\cos\ \pi

a)

00

b)

11

c)

−1-1

d)

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

10.

sin⁡ π\sin\ \pi

a)

00

b)

11

c)

−1-1

d)

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

11.

cos⁡ π2\cos\ \frac{\pi}{2}

a)

00

b)

11

c)

−1-1

d)

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

12.

cos⁡ 3π2\cos\ \frac{3\pi}{2}

a)

00

b)

11

c)

−1-1

d)

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

13.

sin⁡ π2\sin\ \frac{\pi}{2}

a)

00

b)

11

c)

−1-1

d)

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

14.

sin⁡ 3π2\sin\ \frac{3\pi}{2}

a)

00

b)

11

c)

−1-1

d)

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

15.

sin⁡ 0\sin\ 0

a)

00

b)

11

c)

−1-1

d)

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

16.

sin⁡ 2π\sin\ 2\pi

a)

00

b)

11

c)

−1-1

d)

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

17.

cos⁡ 2π\cos\ 2\pi

a)

00

b)

11

c)

−1-1

d)

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

18.

cos⁡ π6\cos\ \frac{\pi}{6}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

19.

sin⁡ π6\sin\ \frac{\pi}{6}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

20.

sin⁡ π4\sin\ \frac{\pi}{4}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

21.

cos⁡ π4\cos\ \frac{\pi}{4}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

22.

cos⁡ π3\cos\ \frac{\pi}{3}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

23.

sin⁡ π3\sin\ \frac{\pi}{3}

a)

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

b)

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

c)

12\frac{1}{2}

d)

11

24.

sec⁡ θ\sec\ \theta

a)

1sin⁡ θ\frac{1}{\sin\ \theta}

b)

1cos⁡ θ\frac{1}{\cos\ \theta}

c)

sin⁡ θcos⁡ θ\frac{\sin\ \theta}{\cos\ \theta}

d)

cos⁡ θsin⁡ θ\frac{\cos\ \theta}{\sin\ \theta}

25.

csc⁡ θ\csc\ \theta

a)

1sin⁡ θ\frac{1}{\sin\ \theta}

b)

1cos⁡ θ\frac{1}{\cos\ \theta}

c)

sin⁡ θcos⁡ θ\frac{\sin\ \theta}{\cos\ \theta}

d)

cos⁡ θsin⁡ θ\frac{\cos\ \theta}{\sin\ \theta}

26.

tan⁡ θ\tan\ \theta

a)

1sin⁡ θ\frac{1}{\sin\ \theta}

b)

1cos⁡ θ\frac{1}{\cos\ \theta}

c)

sin⁡ θcos⁡ θ\frac{\sin\ \theta}{\cos\ \theta}

d)

cos⁡ θsin⁡ θ\frac{\cos\ \theta}{\sin\ \theta}

27.

lim⁡x→af(x) \lim_{x\rightarrow a}f\left(x\right)\ exists

a)

Plug in a

b)

lim⁡x→a+ f(x)=lim⁡x→a− f(x)\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)

c)

lim⁡x→af(x)=f(a)\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)

d)

f(a)f\left(a\right) exists

28.

Condition for IVT

a)

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

b)

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

c)

lim⁡x→af(x) \lim_{x\rightarrow a}f\left(x\right)\ exists

d)

lim⁡x→a+ f(x)=lim⁡x→a− f(x)\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(a)<f(c)<f(b)f\left(a\right)<f\left(c\right)<f\left(b\right)

b)

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

f′(c)=f(b)−f(a)b−af'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}

c)

lim⁡x→af(x)\lim_{x\rightarrow a}f\left(x\right) exists

f(a)f\left(a\right) exists
lim⁡x→af(x)=f(a)\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)

d)

lim⁡x→a+ f(x)=lim⁡x→a− f(x)\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(a)<f(c)<f(b)f\left(a\right)<f\left(c\right)<f\left(b\right)

b)

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

f′(c)=f(b)−f(a)b−af'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}

c)

lim⁡x→af(x)\lim_{x\rightarrow a}f\left(x\right) exists

f(a)f\left(a\right) exists
lim⁡x→af(x)=f(a)\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)

d)

lim⁡x→a+ f(x)=lim⁡x→a− f(x)\lim_{x\rightarrow a^{+\ }}f\left(x\right)=\lim_{x\rightarrow a^{-\ }}f\left(x\right)

31.

Average Rate of Change

a)

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

b)

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

c)

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

d)

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

32.

Instantaneous Rate of Change

a)

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

b)

b−af(b)−f(a)\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′(a)=0f'\left(a\right)=0

c)

Derivative exists

d)

Limit exists

35.

Horizontal Tangent Line

a)

Derivative is undefined

b)

f′(a)=0f'\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′(a)=0f'\left(a\right)=0

or undefined

c)

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

or undefined

d)

f′(a)=0f'\left(a\right)=0

37.

ff is increasing

a)

f′>0f'>0

b)

f′<0f'<0

c)

f′′>0f''>0

d)

f′′<0f''<0

38.

ff is decreasing

a)

f′>0f'>0

b)

f′<0f'<0

c)

f′′>0f''>0

d)

f′′<0f''<0

39.

ff is concave up

a)

f′f' increasing

f′′<0f''<0

b)

f′f' decreasing

f′′>0f''>0

c)

f′f' increasing

f′′>0f''>0

d)

f′f' decreasing

f′′<0f''<0

40.

ff is concave down

a)

f′f' increasing

f′′<0f''<0

b)

f′f' decreasing

f′′>0f''>0

c)

f′f' increasing

f′′>0f''>0

d)

f′f' decreasing

f′′<0f''<0

41.

ff has a relative maximum

a)

f′=0 or undef.f'=0\ or\ undef.

and changes

+ to −+\ to\ -

b)

f′=0 or undef.f'=0\ or\ undef.

and changes

− to +-\ to\ +

c)

f′′=0 or undef.f''=0\ or\ undef.

and changes

+ to −+\ to\ -

d)

f′′=0 or undef.f''=0\ or\ undef.

and changes

− to +-\ to\ +

42.

ff has a relative minimum

a)

f′=0 or undef.f'=0\ or\ undef.

and changes

+ to −+\ to\ -

b)

f′=0 or undef.f'=0\ or\ undef.

and changes

− to +-\ to\ +

c)

f′′=0 or undef.f''=0\ or\ undef.

and changes

+ to −+\ to\ -

d)

f′′=0 or undef.f''=0\ or\ undef.

and changes

− to +-\ to\ +

43.

ff has an inflection point

a)

f′f' has a

relative max or min

b)

f′′f'' has a

relative max or min

c)

f′′=0 or undef.f''=0\ or\ undef.

and changes

signs

d)

f′=0 or undef.f'=0\ or\ undef.

and changes

signs

44.

ddxtan⁡ x\frac{d}{dx}\tan\ x

a)

sec⁡2x\sec^2x

b)

−sec⁡2x-\sec^2x

c)

sec⁡ x ⋅tan⁡ x\sec\ x\ \cdot\tan\ x

d)

csc⁡ x ⋅tan⁡ x\csc\ x\ \cdot\tan\ x

45.

ddxcot⁡ x\frac{d}{dx}\cot\ x

a)

csc⁡2x\csc^2x

b)

−csc⁡2x-\csc^2x

c)

sec⁡ x ⋅cot⁡ x\sec\ x\ \cdot\cot\ x

d)

−csc⁡ x ⋅cot⁡ x-\csc\ x\ \cdot\cot\ x

46.

ddxsec⁡ x\frac{d}{dx}\sec\ x

a)

tan⁡2x\tan^2x

b)

sec⁡ x⋅cot⁡ x\sec\ x\cdot\cot\ x

c)

sec⁡ x ⋅tan⁡ x\sec\ x\ \cdot\tan\ x

d)

csc⁡ x ⋅tan⁡ x\csc\ x\ \cdot\tan\ x

47.

ddxcsc⁡ x\frac{d}{dx}\csc\ x

a)

cot⁡2x\cot^2x

b)

−csc⁡ x⋅cot⁡ x-\csc\ x\cdot\cot\ x

c)

csc⁡ x ⋅tan⁡ x\csc\ x\ \cdot\tan\ x

d)

−csc⁡ x ⋅tan⁡ x-\csc\ x\ \cdot\tan\ x

48.

ddxcsc⁡ x\frac{d}{dx}\csc\ x

a)

cot⁡2x\cot^2x

b)

−csc⁡ x⋅cot⁡ x-\csc\ x\cdot\cot\ x

c)

csc⁡ x ⋅tan⁡ x\csc\ x\ \cdot\tan\ x

d)

−csc⁡ x ⋅tan⁡ x-\csc\ x\ \cdot\tan\ x

49.

∫abf′(x)dx\int_a^bf'\left(x\right)dx

a)

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

b)

f′(b)−f′(a)f'\left(b\right)-f'\left(a\right)

c)

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

d)

f′(a)−f′(b)f'\left(a\right)-f'\left(b\right)

50.

Average Value

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)

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

d)

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

51.

Displacement

a)

∫abv(t)dt\int_a^bv\left(t\right)dt

b)

∫aba(t)dt≈\int_a^ba\left(t\right)dt\approx

c)

∫ab∣v(t)∣dt\int_a^b\left|v\left(t\right)\right|dt

d)

x(a)+∫abv(t)dtx\left(a\right)+\int_a^bv\left(t\right)dt

52.

Total Distance Traveled

a)

∫v(t)dt\int_{ }^{ }v\left(t\right)dt

b)

∫a(t)dt\int_{ }^{ }a\left(t\right)dt

c)

∫ab∣v(t)∣dt\int_a^b\left|v\left(t\right)\right|dt

d)

x(a)+∫abv(t)dtx\left(a\right)+\int_a^bv\left(t\right)dt

53.

∫ 1x dx\int_{ }^{ }\ \frac{1}{x}\ dx

a)

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

b)

ln⁡ x+C\ln\ x+C

c)

ln⁡∣x∣+C\ln\left|x\right|+C

54.

∫ sec⁡xtan⁡x dx\int_{ }^{ }\ \sec x\tan x\ dx

a)

sec⁡ x+C\sec\ x+C

b)

tan⁡ x+C\tan\ x+C

c)

−sec⁡ x+C-\sec\ x+C

d)

tan⁡2x+C\tan^2x+C

55.

∫ sec⁡2x dx\int_{ }^{ }\ \sec^2x\ dx

a)

sec⁡ x+C\sec\ x+C

b)

tan⁡ x+C\tan\ x+C

c)

sec⁡ xtan⁡x+C\sec\ x\tan x+C

d)

tan⁡2x+C\tan^2x+C

56.

∫ csc⁡xcot⁡x dx\int_{ }^{ }\ \csc x\cot x\ dx

a)

−csc⁡ x+C-\csc\ x+C

b)

−cot⁡ x+C-\cot\ x+C

c)

csc⁡ x+C\csc\ x+C

d)

cot⁡2x+C\cot^2x+C

57.

∫ csc⁡2x dx\int_{ }^{ }\ \csc^2x\ dx

a)

−csc⁡ x+C-\csc\ x+C

b)

−cot⁡ x+C-\cot\ x+C

c)

csc⁡ xcot⁡x+C\csc\ x\cot x+C

d)

cot⁡2x+C\cot^2x+C

58.

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

a)

f(x)f\left(x\right)

b)

f′(x)f'\left(x\right)

c)

f(a)f\left(a\right)

d)

00

59.

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

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

d)

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

60.

∫axdx\int_{ }^{ }\text{}a^xdx  

a)

∫axln⁡a+C\int_{ }^{ }\frac{a^x}{\ln a}+C  

b)

axln⁡a+C\frac{a^x}{\ln a}+C  

c)

axln⁡a\frac{a^x}{\ln a}  

d)

ax+Ca^x+C  

61.

∫1a2−u2du\int_{ }^{ }\frac{1}{\sqrt{a^2-u^2}\text{}}du  

a)

sin⁡−1ua+C\sin^{-1}\frac{u}{a}+C  

b)

1atan⁡−1ua+C\frac{1}{a}\tan^{-1}\frac{u}{a}+C  

c)

1asec⁡−1∣u∣a+C\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C  

62.

∫1u2+a2du\int\frac{1}{u^2+a^2}du  

a)

sin⁡−1ua+C\sin^{-1}\frac{u}{a}+C  

b)

1atan⁡−1ua+C\frac{1}{a}\tan^{-1}\frac{u}{a}+C  

c)

1asec⁡−1∣u∣a+C\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C  

63.

∫1uu2−a2du\int_{ }^{ }\frac{1}{u\sqrt{u^2-a^2}}du   

a)

sin⁡−1ua+C\sin^{-1}\frac{u}{a}+C  

b)

1atan⁡−1ua+C\frac{1}{a}\tan^{-1}\frac{u}{a}+C  

c)

1asec⁡−1∣u∣a+C\frac{1}{a}\sec^{-1}\frac{\left|u\right|}{a}+C  

64.

Exponential Growth:

a)

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

b)

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

c)

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

d)

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

65.

Area between two curves:

a)

∫abf(x)−g(x)dx\int_a^bf\left(x\right)-g\left(x\right)dx

b)

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

c)

∫abf(x)g(x)dx\int_a^bf\left(x\right)g\left(x\right)dx

d)

∫abf(x)dx\int_a^bf\left(x\right)dx

66.

∫aaf(x)dx\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→0 f(x+h)−f(x)h\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}

b)

lim⁡h→0 f(h)−f(x)h\lim_{h\rightarrow0}\ \frac{f\left(h\right)-f\left(x\right)}{h}

c)

lim⁡h→0 f(x+h)+f(x)h\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)+f\left(x\right)}{h}

d)

lim⁡h→0 f(h)+f(x)h\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′(c)=f(b)−f(a)b−af'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}

b)

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

c)

f(c)=f′(b)−f′(a)b−af\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}

d)

f′(c)=f′(b)−f′(a)b−af'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}

70.

Volume using discs revolving around horizontal line. 

a)

π∫x=ax=b(top −bottom)2dx  \pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \  

b)

π∫x=ax=b(top −bottom)dx  \pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \  

c)

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

d)

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

71.

Volume using discs revolving around vertical line. 

a)

π∫y=ay=b(right −left)2dy  \pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \  

b)

π∫y=ay=b(right −left)dy  \pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \  

c)

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

d)

∫y=ay=b(right −left)dy  \int_{y=a}^{y=b}\left(right\ -left\right)dy\ \  

72.

Volume using washers revolving around horizontal line. 

a)

π∫x=ax=bR2−r2 dx  \pi\int_{x=a}^{x=b}R^2-r^2\ dx\ \  

b)

π∫x=ax=b(R−r)2 dx  \pi\int_{x=a}^{x=b}\left(R-r\right)^{2\ }dx\ \  

c)

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

d)

∫x=ax=bR2 −r2 dx  \int_{x=a}^{x=b}R^{2\ }-r^{2\ }dx\ \  

73.

Volume using washers revolving around vertical line.

a)

π∫y=ay=bR2−r2 dy  \pi\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \

b)

π∫y=ay=b(R−r)2dy  \pi\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \

c)

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

d)

∫y=ay=bR2−r2 dy  \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: ddxf(x)g(x)\frac{\text{d}}{\text{d}x}\frac{f\left(x\right)}{g\left(x\right)}  =

a)

f′(x)g(x)−g′(x)f(x)(g(x))2\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)

g′(x)f(x)−f′(x)g(x)(g(x))2\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)

f′(x)g(x)+g′(x)f(x)(g(x))2\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)

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

77.

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

ddxax\frac{d}{dx}a^x  =

a)

x⋅ax−1x\cdot a^{x-1}  

b)

axln⁡aa^x\ln a  

c)

axa^x  

d)

axln⁡ea^x\ln e  

78.

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

ddxlog⁡ax=\frac{\text{d}}{\text{d}x}\log_ax=  

a)

1xln⁡a\frac{1}{x\ln a}  

b)

1xln⁡e\frac{1}{x\ln e}  

c)

1x\frac{1}{x}  

d)

1aln⁡x\frac{1}{a\ln x}  

79.
a)
speed
b)
acceleration
c)
displacement
d)
total distance
80.

V=∫ab(top−bottom)2dxV=\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=π8∫ab(top−bottom)2dxV=\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=34∫ab(top−bottom)2dxV=\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=12∫ab(top−bottom)2dxV=\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=14∫ab(top−bottom)2dxV=\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 
cos 2 x + sin 2 x=  
a)
1
b)
csc 2 x + sec 2 x
c)
sin 2 x
d)
1 - sin 2 x
86.

Match the following

Categorize the following

+ velocity & + acc.

- velocity & + acc.

- velocity & - acc.

+ velocity & - acc.

Speed increasing
Speed decreasing

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