Free Printable Unit 1 Review

1.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow-3}\left[f\left(x\right)g\left(x\right)\right]$

b)

$\lim_{x\rightarrow1}\left[g\left(x\right)-f\left(x-3\right)\right]$

c)

$\lim_{x\rightarrow-2}\left[g\left(g\left(x\right)\right)\right]$

2.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow1}\left[g\left(f\left(x+1\right)\right)\right]$

b)

$\lim_{x\rightarrow-2}\left[f\left(g\left(x\right)\right)\right]$

c)

$\lim_{x\rightarrow2}\left[f\left(f\left(x\right)\right)\right]$

3.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow1}\left[f\left(x\right)g\left(x\right)\right]$

b)

$\lim_{x\rightarrow1}\left[-f\left(x\right)f\left(x-3\right)\right]$

c)

$\lim_{x\rightarrow0}\left[f\left(g\left(x\right)\right)\right]$

4.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow1}\left[f\left(x\right)+g\left(x-5\right)\right]$

b)

$\lim_{x\rightarrow-2}\left[f\left(x\right)+g\left(x-1\right)\right]$

c)

$\lim_{x\rightarrow-2}\left[f\left(x\right)+g\left(x\right)\right]$

5.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow0}\left[g\left(x\right)\right]$

b)

$\lim_{x\rightarrow\infty}\left[g\left(x\right)\right]$

c)

$\lim_{x\rightarrow a}f\left(x\right)=2$ , then a=?

6.

Using the provided graphs of f(x) and g(x), evaluate each limit below. Two have the same answer and one is different. Which of these limits has a different answer compared to the other two?

a)

$\lim_{x\rightarrow1}\left[2g\left(x-4\right)-f\left(x\right)\right]$

b)

$\lim_{x\rightarrow\infty}\left[f\left(x\right)-2g\left(x\right)\right]$

c)

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

7.

$\lim_{x\rightarrow0}\left(\frac{x}{x^2-x}\right)$

a)

DNE

b)

0

c)

1

d)

-1

8.

Which of the following are true for f(x)?
I. $\lim_{x\rightarrow3}f\left(x\right)$ does not exist.
II. f(x) is continuous at x=3.
III. The line x=3 is a vertical asymptote.

a)

I only

b)

II only

c)

III only

d)

I and II

e)

I and III

9.

$\lim_{x\rightarrow25}\left[\frac{\sqrt{x}-5}{x-25}\right]$

a)

0

b)

1/25

c)

1/10

d)

1/5

e)

DNE

10.

Suppose $\lim_{x\rightarrow2}f\left(x\right)=5$ , $\lim_{x\rightarrow2}g\left(x\right)=6$ , and $f\left(x\right)\le h\left(x\right)\le g\left(x\right)$ for all x. Which of these must be TRUE?

a)

$f\left(2\right)=5$

b)

$\lim_{x\rightarrow2}h\left(x\right)=5$

c)

$\lim_{x\rightarrow2}h\left(x\right)=6$

d)

The squeeze theorem cannot be applied.

11.

If f(x) is continuous on [2,6] with f(2)=20 and f(6)=10, then IVT says which of the following is true?

a)

f(x)=25 does not have a solution on [2,6]

b)

f(x)=17 has a solution on [2,6]

c)

f(x)=0 has a solution on [2,6]

d)

IVT does't apply

12.

$\lim_{x\rightarrow4}\left(\frac{x+6}{x^2-6x+8}\right)=$

a)

DNE

b)

1/24

c)

3/4

d)

0

13.

$\lim_{x\rightarrow-\infty}\left(\frac{3x+2}{\sqrt{x^2+4}}\right)=$

a)

$-\infty$

b)

-3

c)

0

d)

3

e)

$\infty$

14.

In general, the maximum number of vertical asymptotes that a graph of function f(x) can have is...

a)

There is no maximum number

b)

1

c)

2

d)

3

15.

If f(x) is continuous for all x, the maximum number of horizontal asymptotes that the graph of f(x) can have is

a)

0

b)

1

c)

2

d)

3

e)

There is no maximum number

16.

If the domain of f(x) is $\left[1,\infty\right)$ with f(1)=0, and the line y=3 is a horizontal asymptote for the graph of f(x), which of the following must be true?

a)

The graph of f(x) never meets the line y=3.

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=3$

c)

f(x) is an increasing function

d)

$\lim_{x\rightarrow1}f\left(x\right)\$ does not exist

17.

If f(x) is continuous on [1,8] and some values of f(x) are given in the table, then which of the following must be true?

a)

$f\left(x\right)=-3$ has a solution in [1,8].

b)

$f\left(x\right)=0$ has a solution in [1,8]

c)

$f\left(x\right)=9$ has a solution in [1,8]

d)

f(x) does not satisfy IVT conditions

18.

$\lim_{x\rightarrow0}f\left(x\right)=$

a)

4

b)

2

c)

1

d)

0

e)

DNE

19.

Which of the following are true?

a)

$f\left(2\right)=1$

b)

$\lim_{x\rightarrow2}f\left(x\right)=1$

c)

$\lim_{x\rightarrow2}f\left(x\right)=3$

d)

$f\left(2\right)=3$

20.

Which of the following are false?

a)

$f\left(4\right)$ is undefined

b)

$f\left(4\right)=-3$

c)

$\lim_{x\rightarrow4}f\left(x\right)\ DNE$

d)

$\lim_{x\rightarrow4^+}f\left(x\right)=2$

e)

$\lim_{x\rightarrow4^+}f\left(x\right)=-3$

21.

$f\left(x\right)$ is not continuous at $x=-7$ because

a)

$\lim_{x\rightarrow-7^-}f\left(x\right)\ne\lim_{x\rightarrow-7^+}f\left(x\right)$

b)

$\lim_{x\rightarrow-7}f\left(x\right)\ne f\left(-7\right)$

c)

$\lim_{x\rightarrow-7}f\left(x\right)$ is infinite

22.

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

a)

0

b)

1

c)

DNE

d)

-1

23.

$\lim_{x\rightarrow2}\left(\frac{\frac{2}{x}-\frac{x}{2}}{x-2}\right)$

a)

DNE

b)

0

c)

-1

d)

-4

24.

Find a "c" such that f(x) is continuous.

a)

There is no such "c" that makes f(x) continuous

b)

64

c)

16

d)

4

e)

2

25.

What are all the asymptotes of $f\left(x\right)=\frac{x-2}{x^2+x-6}$

a)

$x=2,\ x=-3$

b)

$x=-3,\ y=0$

c)

$y=-3,\ x=0$

d)

$x=-3$

26.

$\lim_{x\rightarrow\infty}\frac{x^{99}-4x^{98}}{e^x+4x^{97}}$

a)

0

b)

$\infty$

c)

1/4

d)

-1

27.

$\lim_{x\rightarrow-\infty}\frac{\ln x+\sin x}{e^x+4x^2}$

a)

0

b)

$\infty$

c)

DNE

d)

$-\infty$

28.

What is $\lim_{x\rightarrow2}f\left(x\right)$ ?

a)

0

b)

1

c)

2

d)

DNE

29.

Which of the following statements is true?

a)

$\lim_{x\rightarrow1}f\left(x\right)=2.5$

b)

$\lim_{x\rightarrow1}f\left(x\right)=3$

c)

$\lim_{x\rightarrow1}f\left(x\right)$ DNE because $\lim_{x\rightarrow1^-}f\left(x\right)$ and $\lim_{x\rightarrow1^+}f\left(x\right)$ DNE

d)

$\lim_{x\rightarrow1}f\left(x\right)$ DNE because $\lim_{x\rightarrow1^-}f\left(x\right)\ne\lim_{x\rightarrow1^+}f\left(x\right)$

30.

Which of the following conclusions is supported by the data in the table?

a)

$\lim_{x\rightarrow4}f\left(x\right)=6$

b)

$\lim_{x\rightarrow4}f\left(x\right)=7$

c)

$\lim_{x\rightarrow4^-}f\left(x\right)=6$ and $\lim_{x\rightarrow4^+}f\left(x\right)=7$

d)

$\lim_{x\rightarrow4^-}f\left(x\right)=7$ and $\lim_{x\rightarrow4^+}f\left(x\right)=6$

31.

What is $\lim_{x\rightarrow2}\left[h\left(x\right)\left(5f\left(x\right)+g\left(x\right)\right)\right]$ ?

a)

-27

b)

-20

c)

28

d)

34

32.

$\lim_{x\rightarrow-4}\frac{x+4}{x^3-16x}=$

a)

0

b)

1/32

c)

1

d)

DNE

33.

Which of the following is equivalent to $\lim_{x\rightarrow2}\left(\frac{x^2-4}{\sqrt{x}-\sqrt{2}}\right)$ ?

a)

$\lim_{x\rightarrow2}\left(x+2\right)\left(\sqrt{x}+\sqrt{2}\right)$

b)

$\lim_{x\rightarrow2}\left(\sqrt{x}+\sqrt{2}\right)$

c)

$\lim_{x\rightarrow2}\left(x\sqrt{x}-2\sqrt{2}\right)$

d)

$\lim_{x\rightarrow2}\left(x+2\right)\left(x^2+4\right)$

34.

If $g\left(x\right)=\sin\left[\frac{\pi}{2}\left(x+2\right)\right]+3$ and $h\left(x\right)=-\frac{1}{4}x^3-\frac{3}{2}x^2-\frac{9}{4}x+3$ , and $g\left(x\right)\le f\left(x\right)\le h\left(x\right)\$ on (-2,0), what is $\lim_{x\rightarrow-1}f\left(x\right)$ ?

a)

3

b)

3.5

c)

4

d)

Cannot be determined from the given information

35.

Which could be a table for the given function?

a)

b)

c)

d)

36.

What are all the values of x for which f has a removable discontinuity?

a)

0 only

b)

1 only

c)

0 and 2

d)

0, 1, and 2

37.

Which of the following statements is false?

a)

f is continuous at x=1

b)

f is continuous at x=2

c)

f is continuous at x=3

d)

f is continuous at x=4

38.

Which of the following is continuous on the interval 0<x<5?

a)

$f\left(x\right)=\frac{x-3}{x^2-9}$

b)

$g\left(x\right)=\frac{x-3}{x^2+9}$

c)

$h\left(x\right)=\ln\left(x-3\right)$

39.

For what value(s) of b is f(x) continuous at x=2?

a)

0 only

b)

2 only

c)

0 and 2

d)

There is no such b

40.

The function g is continuous at all x except x=4. if $\lim_{x\rightarrow4}g\left(x\right)=\infty$ which of the following statements about g must be true?

a)

$g\left(4\right)=\infty$

b)

The line x=4 is a horizontal asymptote for g

c)

The line x=4 is a vertical asymptote for g

d)

The line y=4 is a vertical asymptote for g.

41.

$f\left(x\right)=\frac{1-5x-2x^2}{3x^2+7}$ Which of the following is a horizontal asymptote of the graph of f?

a)

$y=-\frac{2}{3}$

b)

$y=\frac{1}{3}$

c)

$y=\frac{2}{3}$

d)

f does not have any horizomtal asymptotes

42.

Which of the following statements, if true, would be sufficient to conclude there exists a number c in the interval [-2,2] such that g(c)=6?

a)

g is defined for all x in the interval [-2,2]

b)

g is increasing for all x in the interval [-2,2]

c)

g is continuous on the interval [-2,2]

43.

$\lim_{x\rightarrow6^+}\frac{\left|x-6\right|}{x-6}$

a)

6

b)

1

c)

- 1

d)

DNE

44.

$\lim_{x\rightarrow8}\frac{\left|6-x\right|}{6-x}$

a)

6

b)

1

c)

- 1

d)

DNE

45.

$\lim_{x\rightarrow-1}\frac{x^3+2x+3}{x+1}$

a)

DNE

b)

5

c)

- 2

d)

4

46.

$\lim_{x\rightarrow-\infty}\left(\frac{4^x+3\cos x}{e^x+5x^{71}}\right)$

a)

0

b)

$\infty$

c)

$\frac{4}{e}$

d)

$\frac{e}{4}$

47.

$\lim_{x\rightarrow-8^+}\frac{1}{x+8}$

a)

0

b)

-1

c)

$\infty$

d)

$-\infty$

48.

Determine what type of discontinuity the function $f\left(x\right)=\frac{x^2-2x-8}{x+1}$ has at $x=-1$

a)

Infinite discontinuity

b)

Removable discontinuity

c)

Jump discontinuity

d)

Oscillating discontinuity

49.

Find the value of c that will make f(x) continuous

a)

-3

b)

-2

c)

-1

d)

0

50.

$\lim_{x\rightarrow4^+}-\frac{1}{x-4}$

a)

$\infty$

b)

$-\infty$

c)

0

d)

1

51.

Identify the type and location of the discontinuity/discontinuities in $f\left(x\right)=\frac{x^2-1}{x-4}$ .

a)

Infinite at x = 4

b)

The function is continuous

c)

Removable at x = 4

d)

Infinite at x=1, -1, and 4

52.

Identify the type and location of the discontinuity/discontinuities in $f\left(x\right)=\frac{x^2+7x+10}{x^2+4x-5}$ .

a)

Removable at x = 5 ; Infinite at x = -1

b)

Removable at x = -5 ; Infinite at x = 1

c)

Infinite at x = 1

d)

Infinite at x = 2

53.

Where are the discontinuities in $f\left(x\right)=\frac{x^2-5x+4}{x^2-4}$ ?

a)

-2

b)

2

c)

4

d)

1

54.

What discontinuity is at x=0 (if there is one?)

a)

jump discontinuity

b)

infinite discontinuity

c)

removable discontinuity

d)

f(x) is continuous

55.

$\lim_{x\rightarrow\infty}\frac{x^{59}+4x^{16}}{x^{58}+5^x}$

a)

0

b)

$\infty$

c)

$-\infty$

d)

$\frac{1}{5}$

56.

Which of the following are horizontal asymptotes of $f\left(x\right)=\frac{3-e^x}{x-2x^3}$

a)

$y=0$

b)

This function has no horizontal asymptotes

c)

$y=\pm\frac{3}{2}$

d)

$y=3$

57.

Given a table of values for the continuous function g(x), determine the value of k that will guarantee g(x) has at least two zeros on the interval [0,5]

a)

-3

b)

0

c)

1.5

d)

3

58.

What type(s) of asymptotes does this function have?

f\left(x\right)=\frac{-3x^2+3}{x^2-4}

a)

Vertical

b)

Horizontal

59.

$\lim_{n\rightarrow\infty}\frac{\sqrt{1+n^2}\left(n^2+2n-1\right)^5}{5n^{11}+1}$

a)

0

b)

$\infty$

c)

1/5

d)

1

60.

$\lim_{x\rightarrow4^+}\frac{x+7}{\left(x-4\right)^2}$

a)

$\infty$

b)

$-\infty$

c)

11

d)

0

61.

$\lim_{x\rightarrow4^-}\frac{x+7}{\left(x-4\right)^2}$

a)

$\infty$

b)

$-\infty$

c)

0

d)

11

62.

$\lim_{x\rightarrow-\infty}\left(\frac{\ln x}{x^2}+2\right)$

a)

$\infty$

b)

2

c)

DNE (not infinite)

d)

$-\infty$

63.

$\lim_{x\to-\infty}\frac{2^x+3x^5}{e^x-2x^5}=$

a)

$\infty$

b)

$\frac{2}{e}$

c)

$0$

d)

$-1$

e)

$-\frac{3}{2}$

Unit 1 Review

Total questions: 63

Worksheet time: 45mins

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