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Limits - Printable Mathematics Worksheets - Wayground

Limits

20 questions

11th - 12th Grade

Mathematics

Limits is a Grade 11–12 mathematics worksheet with 20 multiple-choice questions focused on evaluating limits and interpreting limits from graphs. Students select algebraic limit values, determine when a limit approaches positive or negative infinity, identify when a limit does not exist, and read limit behavior from presented function graphs. This free printable worksheet helps students apply limit notation and distinguish among finite results, infinite behavior, and DNE conclusions in a structured practice format. The graph-based questions require students to use visual evidence rather than rely only on symbolic evaluation, reinforcing the connection between a function’s graph and its limiting behavior. It is suitable for guided practice, independent review, or a formative check after introducing limits. A complete answer key is included for efficient review and grading.

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Worksheets

Limits

Total questions: 20

Name
Class
Date
1.

Find lim⁡x→01+x−1x\lim_{x\rightarrow0}\frac{\sqrt{1+x}-1}{\text{x}} . 

a)

12\frac{1}{2}  

b)

14\frac{1}{4}  

c)

DNE

d)

0

2.

Evaluate the limit

a)

-1

b)

0

c)

∞

d)

-∞

e)

DNE

3.

Evaluate the limit

a)

-1

b)

0

c)

∞

d)

-∞

e)

DNE

4.

Evaluate the limit

a)

-1

b)

0

c)

2

d)

4

e)

DNE

5.

Evaluate the limit

a)

-1

b)

0

c)

2

d)

4

e)

DNE

6.

Evaluate the limit

a)

-1

b)

0

c)

2

d)

4

e)

DNE

7.

Evaluate the limit

a)

-1

b)

0

c)

2

d)

4

e)

DNE

8.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→−1f(f(x))?\lim_{x\rightarrow-1}f\left(f\left(x\right)\right)?  

a)

1

b)

2

c)

5

d)

dne

9.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→−1f(x)?\lim_{x\rightarrow-1}f\left(x\right)?  

a)

1

b)

2

c)

5

d)

dne

10.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→2f(x)?\lim_{x\rightarrow2}f\left(x\right)?  

a)

1

b)

2

c)

5

d)

dne

11.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→2+f(x)?\lim_{x\rightarrow2+}f\left(x\right)?  

a)

1

b)

2

c)

5

d)

dne

12.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→−2f(f(x))?\lim_{x\rightarrow-2}f\left(f\left(x\right)\right)?  

a)

1

b)

2

c)

5

d)

dne

13.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→0f(f(x))?\lim_{x\rightarrow0}f\left(f\left(x\right)\right)?  

a)

1

b)

2

c)

5

d)

dne

14.

The graph of the function, f(x) is shown in the graph. What is lim⁡x→3f(f(x))?\lim_{x\rightarrow3}f\left(f\left(x\right)\right)?  

a)

1

b)

2

c)

5

d)

dne

15.

The graph of the function, f(x) is shown. What is lim⁡x→2+f(x)?\lim_{x\rightarrow2+}f\left(x\right)?  

a)

1

b)

3

c)

4

d)

dne

16.

The graph of the function, f(x) is shown. What is lim⁡x→2−f(x)?\lim_{x\rightarrow2-}f\left(x\right)?  

a)

1

b)

3

c)

4

d)

dne

17.

The graph of the function, f(x) is shown. What is f(2)?f\left(2\right)?  

a)

1

b)

3

c)

4

d)

dne

18.

The graph of the function, f(x) is shown above. What is lim⁡x→2+f(x)?\lim_{x\rightarrow2+}f\left(x\right)?  

a)

3

b)

2

c)

1

d)

dne

e)

4

19.

The graph of the function, f(x) is shown above. What is lim⁡x→2−f(x)?\lim_{x\rightarrow2-}f\left(x\right)?  

a)

3

b)

2

c)

1

d)

dne

e)

4

20.

The graph of the function, f(x) is shown above. What is lim⁡x→2f(x)?\lim_{x\rightarrow2}f\left(x\right)?  

a)

3

b)

2

c)

1

d)

dne

e)

4

Answer Key

Limits

Total questions: 20

1.
a)

12\frac{1}{2}  

2.
d)

-∞

3.
c)

∞

4.
e)

DNE

5.
d)

4

6.
b)

0

7.
a)

-1

8.
d)

dne

9.
b)

2

10.
d)

dne

11.
b)

2

12.
b)

2

13.
b)

2

14.
b)

2

15.
a)

1

16.
c)

4

17.
b)

3

18.
a)

3

19.
c)

1

20.
d)

dne

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FAQs

What does this Limits worksheet help students practice?

This Grade 11–12 mathematics worksheet uses 20 multiple-choice questions to practise evaluating limits and interpreting limits from graphs. Students distinguish finite values from positive infinity, negative infinity, and DNE results, then use graph behavior to identify the requested limit.

How can I use this worksheet to teach evaluating limits and reading graphs?

Introduce the worksheet by reviewing that a limit describes the value a function approaches, then have students explain why an answer is a finite number, infinity, or DNE. For the graph-based multiple-choice items, ask students to trace the function toward the relevant x-value and compare the left- and right-hand behavior before selecting an option.

What mistakes should I watch for when students complete this limits worksheet?

Students may confuse the function’s plotted value with the value the graph approaches, leading to errors on the graph-based limit questions. They may also select a finite option when the behavior is unbounded, overlook a DNE result when the two sides do not agree, or reverse positive and negative infinity.

How do I assign and grade this Limits worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 20 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the multiple-choice options and graph-based prompts are easier to follow. You can also apply a dyslexia-friendly font or translate the worksheet into another language while preserving its limits practice format.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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