# Worksheet: Existence of Limits

Q1:

Discuss the existence of given

• AThe limit does not exist because exists, but does not exist.
• BThe limit does not exist because exists, but does not exist.
• CThe limit does not exist because both and exist, but are not equal.
• DThe limit exists and equals 210.
• EThe limit exists and equals .

Q2:

Given that find , if it exists.

• A
• B1
• C
• Ddoes not exist
• E

Q3:

Suppose that What can be said about the existence of ?

• A The limit exists and equals 1.
• B The limit does not exist because .
• C The limit exists and equals 0.
• D The limit exists and equals .

Q4:

Discuss the existence of given

• AThe limit exists and equals 0.
• BThe limit does not exist because .
• CThe limit exists and equals .
• DThe limit exists and equals 1.
• EThe limit exists and equals .

Q5:

Discuss the existence of given

• AThe limit exists and equals .
• BThe limit exists and equals .
• CThe limit does not exist because .
• DThe limit exists and equals 1.

Q6:

Discuss the existence of given

• AThe limit exists and equals.
• BThe limit exists and equals.
• CThe limit exists and equals.
• DThe limit does not exist because.

Q7:

Discuss the existence of given

• AThe limit exists and equals 9.
• BThe limit exists and equals 0.
• CThe limit exists and equals .
• DThe limit does not exist.

Q8:

Given that find .

• A
• B5
• C
• D1

Q9:

Discuss the existence of given

• AThe limit exists and equals .
• BThe limit exists and equals 20.
• CThe limit does not exist because does not exist.
• DThe limit does not exist because .

Q10:

Discuss the existence of given

• A does not exist because exist, but does not exist.
• B does not exist because .
• C does not exist because exist, but does not exist.
• D exist and equals 3.

Q11:

Discuss the existence of given

• AThe limit exists and equals .
• BThe limit exists and equals 5.
• CThe limit does not exist because does not exist.
• DThe limit does not exist because .
• EThe limit does not exist because does not exist.

Q12:

Suppose that What can be said about the existence of .

• A The limit exists and equals .
• B The limit does not exist because .
• C The limit exists and equals 5.
• D The limit exists and equals .

Q13:

Describe the limit as for the following function:

• AThe limit exists and equals .
• BThe limit exists and equals .
• CThe limit exists and equals .
• DThe limit does not exist because .
• EThe limit exists and equals .

Q14:

Discuss the existence of the limit as given

• AThe limit exists and equals .
• BThe limit does not exist because
• CThe limit exists and equals .
• DThe limit exists and equals.

Q15:

Determine if it exists, where

• A
• B1
• C4
• D5

Q16:

Determine , where

Q17:

Discuss the existence of given .

• A The limit does not exist because .
• B The limit exists and equals .
• C The limit does not exist because does not exist.
• D The limit exists and equals .
• E The limit does not exist because does not exist.

Q18:

Given that determine .

• A
• B2
• C
• D

Q19:

Given that and exists, determine the possible values of .

• A
• B
• C
• D

Q20:

Given that the function has a limit when , determine the values of and .

• A ,
• B ,
• C ,
• D ,

Q21:

Discuss the existence of given

• AThe limit exists and equals.
• BThe limit exists and equals.
• CThe limit does not exist because does not exist.
• DThe limit does not exist because.
• EThe limit does not exist because does not exist.

Q22:

Suppose that What can be said about the existence of ?

• AThe limit exists and equals .
• BThe limit does not exist because .
• CThe limit exists and equals .

Q23:

Find given

• A10
• B28
• C

Q24:

Discuss the existence of given

• AThe limit exists and equals 0.
• BThe limit does not exist because .
• CThe limit exists and equals 3.
• DThe limit exists and equals 5.
• EThe limit exists and equals 7.

Q25:

Given that find .