Free Printable TEST REVIEW || Unit 1 - Tangents, Secants & Limits

1.

a)

A

b)

B

c)

C

d)

D

2.

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

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

3.

Which of the following best describes the continuity at x = -4?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

4.

Let f be a function that is continuous on the interval (1, 10). If f(2) = -5 , f(5) = 5 and f(9) = -5, which must be true?

I. f(x) has a least 2 zeros
II. For some c, 2 < c < 9, f(c) = 3
III. The graph of f(x) has a horizontal tangent

a)

I. only

b)

I. and II.

c)

I. , II. and III.

d)

II. and III.

5.

Which of the following is true?

a)

b)

c)

d)

6.

$\lim_{x\rightarrow-2^+}f\left(x\right)$

a)

DNE

b)

-2

c)

3

d)

-4

7.

$\lim_{x\rightarrow-3}\sqrt{7x+22}$

a)

$\sqrt{43}$

b)

1

c)

DNE

d)

3

8.

Find the average rate of change of Pete's height from 3 years old to 5 years old.

a)

2 inches per year

b)

8 inches per year

c)

2 years

d)

4 inches per year

9.

instantaneous rate of change means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

slope of a secant line

d)

potato

10.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

11.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

12.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

13.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

14.

Is the function continuous at x = 4?

a)

Yes

b)

No; because f(4) isn't defined

c)

No; the limit at x=4 doesn't exist

d)

No; the limit at x=4 doesn't equal f(4)

15.

For a limit to exist, the left and the right hand limits must be equal.

a)

true

b)

false

16.

Find where the function is continuous

a)

(-∞,-1)(-1,3)(3,∞)

b)

(-∞,∞)

c)

(-∞,-3)(-3,1)(1,∞)

d)

(-∞,-2)(-2,3)(3,∞)

17.

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

18.

Consider the piecewise function for f(x) as shown.

For what value of the constant c is f continuous for all real numbers?

a)

0

b)

$-\ 1$

c)

$-\ \frac{1}{4}$

d)

$4$

e)

$\frac{4}{5}$

19.

Evaluate.

a)

0

b)

1/2

c)

2

d)

The limit does not exist

20.

Evaluate

a)

1/3

b)

-1/3

c)

The limit does not exist

d)

0

21.

Find the average rate of change on the interval $\left[a,a+h\right]$

a)

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

b)

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

c)

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

d)

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

22.

Given the following graph with tangent lines, at which

x-value is the derivative equal to zero?

a)

$x=-8$

b)

$x=-5$

c)

$x=-1.7$

d)

$x=1$

23.

Write the equation of the tangent line drawn at
$x=1$

a)

$y=1$

b)

$x=1$

c)

undefined

d)

$y=2x+1$

24.

The derivative is...

a)

slope of the secant line

b)

slope of the tangent line

c)

slope of the cosecant line

d)

slope of the normal line

25.

$\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....$

a)

0

b)

5

c)

$\infty$

d)

$\frac{5}{2}$

e)

$\frac{2}{5}$

26.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[f\left(x\right)\cdot5g\left(x\right)\right]$

a)

-30

b)

-40

c)

60

d)

-80

27.

Evaluate the limit.

a)

$\frac{7}{8}$

b)

$1$

c)

$7$

d)

$DNE$

28.

Find $\lim_{x\rightarrow\frac{\text{1}}{\text{2}}}4x\left(x-\frac{\text{1}}{\text{4}}\right)$ .

a)

$\frac{\text{1}}{\text{2}}$

b)

1

c)

$\frac{\text{1}}{\text{8}}$

d)

$\frac{\text{3}}{\text{2}}$

29.

a)

DNE

b)

1

c)

2.9

d)

3

30.

Which graph shows inverse functions?

a)

b)

c)

d)

31.

Which line is used to reflect a function, in order to find its inverse function?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

32.

Which is the inverse of the table?

a)

b)

c)

d)

33.

At which x-value is f continuous but not differentiable?

a)

a

b)

b

c)

c

d)

d

34.

Give the interval of continuity for the graph provided.

a)

(-∞, 2)U(2,6]

b)

(-∞, 2]U(2,6]

c)

(-∞, 2)U[2,6]

d)

(-∞, 2)U(2,6)

35.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

TEST REVIEW || Unit 1 - Tangents, Secants & Limits

Total questions: 35

Worksheet time: 2hrs 1mins

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