# Worksheet: Limits and Limit Notation

In this worksheet, we will practice using limit notation and exploring the concept of a limit.

Q1:

What is the correct notation that describes the following statement?

As approaches 0 , approaches .

• A
• B
• C
• D

Q2:

What does the notation mean?

• AAs gets closer and closer to 5 , gets closer and closer to 2 .
• BAs gets closer and closer to 2 , gets closer and closer to 5 .
• CThe value of at is equal to the value of at .
• DThe value of the function is 2 at .
• E is undefined at and at .

Q3:

The following table gives the values of the function at several values of .

 𝑥 𝑓(𝑥) 2.99 2.999 2.9999 2.9999 3.00001 3.0001 3.001 3.01 −5.89 −5.91 −5.97 −5.99 −6.0002 −6.007 −6.01 −6.02

What does the table suggest about the value of ?

• AThe value of the limit equals .
• BThe value of the limit equals .
• CThe value of the limit equals 2.
• DThe value of the limit equals 3.

Q4:

The following table gives the values of the function at several values of .

 𝑥 𝑓(𝑥) −4.895 −4.902 −4.979 −4.9999 −5.0001 −5.0004 −5.007 −5.02 −14.01 −14.005 −14.003 −14.0001 −13.9999 −13.998 −13.92 −13.895

What does the table suggest about the value of ?

• AThe value of the limit does not exist.
• BThe value of the limit equals .
• CThe value of the limit equals .
• DThe value of the limit equals .
• EThe value of the limit equals .

Q5:

True or False: If , then it is possible that the function could be undefined at .

• AFalse
• BTrue

Q6:

True or False: If , then must be equal to .

• AFalse
• BTrue

Q7:

The following figure represents the graph of the function . What does the graph suggest about the value of ?

• A
• B
• C
• D does not exist.
• E

Q8:

The following figure represents the graph of the function . What does the graph suggest about the value of ?

• AThe limit does not exist.
• BThe value of the limit equals 3.
• CThe value of the limit equals .
• DThe value of the limit equals .
• EThe value of the limit equals 2.

Q9:

The following figure is the graph of the function , where . What is the value of ?

• A is undefined.
• B
• C
• D
• E

What does the graph suggest about the value of ?

• A does not exist.
• B
• C
• D
• E

Q10:

The following figure is the graph of the function , where . What is the value of ?

• A
• B is undefined.
• C
• D
• E

What does the graph suggest about the value of ?

• A
• B
• C
• D
• E does not exist.

Q11:

Which of the following statements is not the same as saying that ?

• A is equal to .
• B approaches 3 as approaches 8 .
• CWe can make as close as we like from 3 by taking sufficiently close to 8 .
• DAs gets closer and closer to 8 , gets closer and closer to 3 .

Q12:

If , what can we say about ?

• A
• B
• C
• DWe cannot draw any conclusions about .
• E

Q13:

Given that , what is the value of ?

• A10
• B20
• C7
• D5
• E13

Q14:

Given that , which of the following statements must be false?

• A is undefined.
• B
• C
• D
• E

Q15:

Given that , which of the following statements must be true?

• A
• B
• C
• D
• ENone of the above