# Worksheet: Limits by Algebraic Simplification

Q1:

Given that , what is ?

• A
• B
• C
• D36

Q2:

Find .

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

Q3:

Find .

• A
• B
• C
• D
• EThe limit doesn’t exist.

Q4:

Find .

Q5:

Find .

• A
• BThe limit doesn’t exist.
• C3
• D

Q6:

Find .

• A0
• B6
• C
• D
• E

Q7:

Find .

• A0
• B
• C
• D
• E

Q8:

Find .

Q9:

Find .

• A
• B
• C
• D

Q10:

Find .

• A
• B0
• C
• D

Q11:

If , determine the values of and .

• A ,
• B ,
• C ,
• D ,

Q12:

Given that determine .

• A5
• B
• C
• D

Q13:

Given that the limit of the function exists when , determine the value of .

• A
• B
• C
• D2

Q14:

Suppose that What can be said about the existence of ?

• A The limit exists and equals 15.
• B The limit does not exist because .
• C The limit exists and equals 13.

Q15:

Given the function , what is true of ?

• A The limit exists and equals .
• B The limit does not exist because .
• C The limit exists and equals 40.

Q16:

Determine .

• A
• B
• C5
• D

Q17:

Given that , determine .

Q18:

Given the function , what is true of ?

• AThe limit exists and equals 45.
• BThe limit exists and equals .
• CThe limit exists and equals 15.
• DThe limit does not exist because .
• EThe limit exists and equals .

Q19:

Determine .

• A
• B1
• C28
• D29
• EThe limit does not exist.

Q20:

If , where determine the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q21:

Determine .

• A
• B26
• C
• D

Q22:

The function has a limit at and . What are the values of and ?

• A ,
• B ,
• C ,
• D ,