Free Printable The Must Knows

1.

The limit is about what the function

a)

approaches

b)

cooks for dinner

c)

equals

d)

posts on Instagram

2.

$\lim_{x\rightarrow c^-}f\left(x\right)$

What is this?

a)

left-hand limit

b)

right-hand limit

c)

chicken limit

d)

beef limit

3.

$\lim_{x\rightarrow c^+}f\left(x\right)$

What is this?

a)

left-hand limit

b)

right-hand limit

c)

Zendaya

d)

Lady Gaga

4.

The limit exists if the left and right hand limits

a)

are not the same

b)

are the same

c)

like each other

d)

poke each other

5.

What is intermediate form?

a)

$\frac{0}{1}$

b)

$\frac{0}{0}$

c)

$\frac{\infty}{1}$

d)

$\frac{\infty}{\infty}$

6.

What do you do?

a)

Multiply numerator but not denominator

b)

Multiply denominator but not numerator

c)

Multiply numerator and denominator

d)

Don't multiply numerator or denominator

7.

$\lim_{x\rightarrow0}\frac{\sin x}{x}$

a)

0

b)

1

c)

-1

d)

$\infty$

8.

$\lim_{x\rightarrow0}\frac{1-\cos x}{x}$

a)

0

b)

1

c)

-1

d)

$\infty$

9.

The Intermediate Value Theorem requires

a)

continuity

b)

differentiability

c)

low carbs

d)

no added sugar

10.

The Intermediate Value guarantees that for every y value between (c, d) there is one ___ between (a, b) that will equal it

a)

x value

b)

y value

c)

boy

d)

girl

11.

If the limit as x approaches 3 is infinity, that means x=3 has a(n)

a)

horizontal asymptote

b)

vertical asymptote

c)

pimple

d)

zit

12.

Continuity requires

a)

the y-value is positive

b)

the y-value exists

c)

the limit exists

d)

the y-value and limit are the same

13.

Limits that approach infinity also reveal

a)

horizontal asmyptotes

b)

vertical asymptotes

c)

bald spots

d)

white hairs

14.

SHORTCUT: If m is less than n, there is

a)

a horizontal asymptote (infinite limit) of 0

b)

a horizontal asymptote (infinite limit) of A/B

c)

no horizontal asymptote (and infinite limit approaches nothing)

d)

no horizontal asymptote (and infinite limit approaches infinity)

15.

SHORTCUT: If m is equal to n, there is

a)

a horizontal asymptote (infinite limit) of 0

b)

a horizontal asymptote (infinite limit) of A/B

c)

no horizontal asymptote (and infinite limit approaches nothing)

d)

no horizontal asymptote (and infinite limit approaches infinity)

16.

SHORTCUT: If m is greater than n, there is

a)

a horizontal asymptote (infinite limit) of 0

b)

a horizontal asymptote (infinite limit) of A/B

c)

no horizontal asymptote (and infinite limit approaches nothing)

d)

no horizontal asymptote (and infinite limit approaches infinity)

17.

The derivative also represents

a)

area under the curve

b)

instantaneous rate of change

c)

slope at a point

d)

slope of the tangent line

18.

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

This means you're trying to find the

a)

the limit of f(x)

b)

the derivative of f(x)

c)

the integral of f(x)

d)

the antiderivative of f(x)

19.

In order for a point to be differentiable, it must also be

a)

continuous

b)

cute

c)

beautiful

d)

hot

20.

When is a function not differentiable?

a)

at a cusp

b)

at a discontinuity

c)

at the origin

d)

at a vertical tangent line

21.

$\frac{d}{dx}\sin\left(x\right)$

a)

$\cos\left(x\right)$

b)

$-\cos\left(x\right)$

c)

$\sec^2\left(x\right)$

d)

$-\sec^2\left(x\right)$

22.

$\frac{d}{dx}\cos\left(x\right)$

a)

$\csc\left(x\right)\cot\left(x\right)$

b)

$-\csc\left(x\right)\cot\left(x\right)$

c)

$\sin\left(x\right)$

d)

$-\sin\left(x\right)$

23.

$\frac{d}{dx}\tan\left(x\right)$

a)

$-\sin\left(x\right)$

b)

$\cos\left(x\right)$

c)

$\sec\left(x\right)\tan\left(x\right)$

d)

$\sec^2\left(x\right)$

24.

$\frac{d}{dx}\csc\left(x\right)$

a)

$-\csc\left(x\right)\cot\left(x\right)$

b)

$\csc\left(x\right)\cot\left(x\right)$

c)

$-\sec\left(x\right)\tan\left(x\right)$

d)

$\sec\left(x\right)\tan\left(x\right)$

25.

$\frac{d}{dx}\sec\left(x\right)$

a)

$\sec^2\left(x\right)$

b)

$-\csc^2\left(x\right)$

c)

$\sec\left(x\right)\tan\left(x\right)$

d)

$-\csc\left(x\right)\cot\left(x\right)$

26.

$\frac{d}{dx}\cot\left(x\right)$

a)

$\csc^2\left(x\right)$

b)

$-\csc^2\left(x\right)$

c)

$\csc\left(x\right)\cot\left(x\right)$

d)

$-\csc\left(x\right)\cot\left(x\right)$

27.

$\frac{d}{dx}e^x$

a)

$e$

b)

$x$

c)

$e^x$

d)

$xe^x$

28.

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

a)

$a^x$

b)

$ax$

c)

$a^x\ln a$

d)

$a^x\log a$

29.

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

a)

$1$

b)

$x$

c)

$\frac{1}{x}$

d)

$-\frac{1}{x}$

30.

$\frac{d}{dx}\log_ax$

a)

$\frac{1}{x}$

b)

$\frac{1}{a}$

c)

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

d)

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

31.

What is the product rule?

a)

$1\ d'1\ +\ 2\ d'2$

b)

$1\ d'1\ -\ 2\ d'2$

c)

$2\ d'1\ +\ 1\ d'2$

d)

$2\ d'1\ -\ 1\ d'2$

32.

What is the quotient rule?

a)

$\frac{l\ d'h\ -\ h\ d'l}{l}$

b)

$\frac{l\ d'h\ -\ h\ d'l}{l^2}$

c)

$\frac{l\ d'h\ +\ h\ d'l}{l}$

d)

$\frac{l\ d'h\ +\ h\ d'l}{l^2}$

33.

What is the chain rule?

a)

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

b)

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

c)

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

d)

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

34.

In implicit differentiation, anytime you take the derivative of y, multiply it with

a)

$x$

b)

$y$

c)

$1$

d)

$\frac{dy}{dx}$

35.

Given f and g are inverse functions and (a, b) is a point on f, then f'(a) is equal to

a)

g'(a)

b)

g'(b)

c)

the reciprocal of f'(a)

d)

the reciprocal of g'(b)

36.

$\frac{d}{dx}\sin^{-1}x$

a)

$\frac{1}{\sqrt[]{1-x^2}}$

b)

$-\frac{1}{\sqrt[]{1-x^2}}$

c)

$\frac{1}{1-x^2}$

d)

$-\frac{1}{1-x^2}$

37.

$\frac{d}{dx}\cos^{-1}x$

a)

$\frac{1}{\sqrt[]{1-x^2}}$

b)

$-\frac{1}{\sqrt[]{1-x^2}}$

c)

$\frac{1}{x^2+1}$

d)

$-\frac{1}{x^2+1}$

38.

$\frac{d}{dx}\tan^{-1}x$

a)

$\frac{1}{\sqrt[]{1+x^2}}$

b)

$\frac{1}{\sqrt[]{1+x^2}}$

c)

$\frac{1}{1+x^2}$

d)

$-\frac{1}{1+x^2}$

39.

$\frac{d}{dx}\csc^{-1}x$

a)

$\frac{1}{\sqrt[]{x^2-1}}$

b)

$-\frac{1}{\sqrt[]{x^2-1}}$

c)

$\frac{1}{\left|x\right|\sqrt[]{x^2-1}}$

d)

$-\frac{1}{\left|x\right|\sqrt[]{x^2-1}}$

40.

$\frac{d}{dx}\sec^{-1}x$

a)

$\frac{1}{\left|x\right|\sqrt[]{x^2-1}}$

b)

$-\frac{1}{\left|x\right|\sqrt[]{x^2-1}}$

c)

$\frac{1}{\left|x\right|\sqrt[]{x^2+1}}$

d)

$-\frac{1}{\left|x\right|\sqrt[]{x^2+1}}$

41.

$\frac{dy}{dx}\cot^{-1}x$

a)

$\frac{1}{1-x^2}$

b)

$-\frac{1}{1-x^2}$

c)

$\frac{1}{1+x^2}$

d)

$-\frac{1}{1+x^2}$

42.

What condition do you need for L'Hospital's rule?

a)

a number divided by zero

b)

a number divided by infinity

c)

discontinuity

d)

indeterminate form

43.

How do you use L'Hospital's Rule to find a limit?

a)

find the derivative of the function then plug in

b)

find the derivative of the numerator and then plug in

c)

find the derivative of the denominator and then plug in

d)

find the derivative of the numerator and denominator separately and then plug in

44.

How do you find the units of the derivative?

a)

x units

b)

y units

c)

x units divided by y units

d)

y units divided by x units

45.

What is the derivative of position?

a)

velocity

b)

speed

c)

acceleration

d)

racecar

46.

What is the derivative of velocity?

a)

velocity

b)

speed

c)

acceleration

d)

marathon

47.

How do you know if something is speeding up?

a)

velocity is positive

b)

acceleration is positive

c)

velocity and acceleration are the same sign

d)

velocity and acceleration are the different signs

48.

How do you know if something is slowing down?

a)

velocity is negative

b)

acceleration is negative

c)

velocity and acceleration are the same sign

d)

velocity and acceleration are the different signs

49.

What is the condition for the Mean Value Theorem?

a)

continuity

b)

differentiability

c)

both continuity and differentiability

d)

no ugly points

50.

The Mean Value Theorem guarantees that for the average rate of change of (a, b) there will be a c between (a, b) that will have the same

a)

average rate of change

b)

instantaneous rate of change

c)

y-value as a

d)

y-value as b

51.

If the first derivative is positive, that means

a)

f is increasing

b)

f is decreasing

c)

f'' is increasing

d)

f'' is decreasing

52.

If the first derivative is negative, that means

a)

f is increasing

b)

f is decreasing

c)

f is positive

d)

f is negative

53.

A relative minimum requires that f'

a)

is zero

b)

is negative

c)

changes from positive to negative

d)

changes from negative to positive

54.

A relative maximum requires that f'

a)

is zero

b)

is negative

c)

changes from positive to negative

d)

changes from negative to positive

55.

If the second derivative is positive, that means

a)

f is concave up

b)

f is concave down

c)

f is increasing

d)

f is decreasing

56.

If the second derivative is negative, that means

a)

f is concave up

b)

f is concave down

c)

f is positive

d)

f is negative

57.

An inflection point requires that f''

a)

is zero

b)

is positive

c)

is negative

d)

changes signs

58.

How do you find the units of the integral?

a)

x units

b)

y units

c)

x units times y units

d)

x units divided by y units

59.

$\int_{ }^{ }$

What can this mean?

a)

find the derivative

b)

find the antiderivative

c)

find the limit

d)

find the area under the curve

60.

This is a

a)

left Riemann sum

b)

right Riemann sum

c)

midpoint Riemann sum

d)

trapezoidal Riemann sum

61.

This is a

a)

left Riemann sum

b)

right Riemann sum

c)

midpoint Riemann sum

d)

trapezoidal Riemann sum

62.

This is a

a)

left Riemann sum

b)

right Riemann sum

c)

midpoint Riemann sum

d)

trapezoidal Riemann sum

63.

This is a

a)

left Riemann sum

b)

right Riemann sum

c)

midpoint Riemann sum

d)

trapezoidal Riemann sum

64.

What is correct about the areas of these regions?

a)

Positive: A, B

Negative: C, D

b)

Positive: A, C

Negative: B, D

c)

Positive: B, C

Negative: A, D

d)

Positive: B, D

Negative: A, C

65.

$\frac{d}{dx}\int_a^bf\left(x\right)dx$

For the Fundamental Theorem of Calculus (part 1), you want

a)

a to be x, and b to be a number

b)

a to be a number, and b to be x

c)

a and b to both be numbers

d)

a and b to both be x

66.

$\frac{d}{dx}\int_a^bf\left(x\right)dx$

For the Fundamental Theorem of Calculus (part 1), if b is 2x, you will have to use

a)

product rule

b)

quotient rule

c)

chain rule

d)

Lau rules!!!

67.

If F is the antiderivative of f, then $\int_a^bf\left(x\right)dx$ is

a)

f(a) - f(b)

b)

f(b) - f(a)

c)

F(a) - F(b)

d)

F(b) - F(a)

68.

When you find an antiderivative, remember to always

a)

write +C

b)

pick your nose

c)

curl your tongue

d)

wiggle your toenails

69.

"y varies directly proportional to x"

a)

$\frac{dy}{dx}=k$

b)

$\frac{dy}{dx}=x$

c)

$\frac{dy}{dx}=kx$

d)

$\frac{dy}{dx}=\frac{k}{x}$

70.

"y varies inversely proportional to x"

a)

$\frac{dy}{dx}=\frac{k}{x}$

b)

$\frac{dy}{dx}=\frac{x}{k}$

c)

$\frac{dy}{dx}=kx$

d)

$\frac{dy}{dx}=\frac{k}{y}$

71.

"y varies directly proportional to itself"

a)

$\frac{dy}{dx}=ky$

b)

$\frac{dy}{dx}=xy$

c)

$\frac{dy}{dx}=\frac{k}{y}$

d)

$\frac{dy}{dx}=\frac{y}{k}$

72.

What is the antiderivative of $\frac{dy}{dx}=ky$ ?

a)

$y=e^{kx}$

b)

$y=Ce^{kx}$

c)

$y=Cek^x$

d)

$y=Cekx$

73.

Given $\frac{dy}{dx}$ , the slope is zero when

a)

the numerator is zero

b)

the denominator is zero

c)

both numerator and denominator are zero

d)

both numerator and denominator are infinity

74.

Given $\frac{dy}{dx}$ , the slope is undefined when

a)

the numerator is zero

b)

the denominator is zero

c)

both numerator and denominator are zero

d)

both numerator and denominator are infinity

75.

How do you find average value?

a)

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

b)

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

c)

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

d)

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

The Must Knows

Total questions: 75

Worksheet time: 38mins

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