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Limits and Continuity Worksheet

Grade 11 Calculus worksheet covering limits, continuity, and related concepts with various question types.

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Grade 11 Math CalculusLimits and Continuity
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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ECCSS.MATH.CONTENT.HSF.BF.A.1.ACCSS.MATH.CONTENT.HSF.BF.B.3

Topics

CalculusLimitsContinuityGrade 11Math
7 sections · Free to use · Printable
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Limits and Continuity Review

Name:

Date:

Score:

Read each question carefully and provide clear, concise answers. Show all your work for full credit.

1. What is the limit of the function f(x) = (x^2 - 4) / (x - 2) as x approaches 2?

a

0

b

2

c

4

d

Does not exist

2. For a function to be continuous at a point 'c', which of the following conditions must be met?

a

f(c) is defined

b

lim f(x) as x->c exists

c

lim f(x) as x->c = f(c)

d

All of the above

3. A function is said to be   at a point if the limit of the function as x approaches that point exists, and the function's value at that point is equal to the limit.

4. If a function has a hole in its graph, it represents a   discontinuity.

5. Consider the function f(x) = |x| / x. Evaluate the left-hand limit, the right-hand limit, and the overall limit as x approaches 0. Is the function continuous at x=0? Explain your reasoning.

-5-4-3-2-112345-5-4-3-2-112345

6. If a function is differentiable at a point, then it must also be continuous at that point.

T

True

F

False

7. A vertical asymptote indicates a point of removable discontinuity.

T

True

F

False

8. Determine the value of 'a' that makes the function continuous at x = 3:

f(x) = { ax^2 - 1, if x < 3

{ 2x + 5, if x >= 3

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