Worksheet: Limits of a Difference of Powers

In this worksheet, we will practice evaluating limits of a difference of powers.

Q1:

Determine .

• AThe limit does not exist.
• B
• C
• D
• E

Q2:

Find .

• AThe limit does not exist.
• B
• C
• D8
• E

Q3:

Find .

• A
• B0
• C
• DThe limit does not exist.
• E4

Q4:

Discuss the existence of given

• A
• B
• C4
• DThe limit does not exist.
• E

Q5:

Find given

• A
• B
• Cdoes not exist
• D
• E

Q6:

Find given

• A1
• B
• C
• D
• E The limit does not exist.

Q7:

Find .

• Ahas no limit
• B
• C
• D
• E

Q8:

Find .

Q9:

Find .

• A
• B0
• C
• D
• E

Q10:

Find .

Q11:

Find .

• AThe limit does not exist.
• B
• C
• D

Q12:

Find .

• A
• B
• C
• D0

Q13:

Given that , determine all the possible values of .

• A
• B
• C
• D
• E

Q14:

Find .

• A0
• B36
• C540
• D108

Q15:

Find .

• A
• B
• CThe limit doesn’t exist.
• D
• E

Q16:

Find .

Q17:

Find .

• A
• B
• CThe limit does not exist.
• D
• E

Q18:

Find .

• A
• Bhas no limit
• C20
• D5
• E

Q19:

Find .

Q20:

Find .

• A
• B
• C
• D
• EThe limit does not exist.

Q21:

Find .

Q22:

Find .

• A16
• B
• CThe limit does not exist.
• D
• E

Q23:

If , what are the values of and ?

• A ,
• B ,
• C ,
• D ,

Q24:

Determine the value of to the nearest hundredth.

Q25:

Given that , find .

• A
• B
• CThe limit does not exist.
• D
• E