# Worksheet: Limits by Algebraic Simplification

Q1:

Given that , what is ?

• A
• B36
• C
• D

Q2:

Find .

• AThe limit doesn’t exist.
• B
• C
• D

Q3:

Find .

• AThe limit doesn’t exist.
• B
• C
• D
• E

Q4:

Find .

Q5:

Find .

• A3
• B
• C
• DThe limit doesn’t exist.

Q6:

Find .

• A
• B
• C
• D0
• E6

Q7:

Find .

• A
• B
• C
• D0
• E

Q8:

Find .

Q9:

Find .

• A
• B
• C
• D

Q10:

Find .

• A
• B
• C
• D0

Q11:

If , determine the values of and .

• A,
• B,
• C,
• D,

Q12:

Given that determine .

• A
• B
• C5
• D

Q13:

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

• A
• B2
• C
• D

Q14:

Suppose that What can be said about the existence of ?

• AThe limit exists and equals 13.
• BThe limit exists and equals 15.
• CThe limit does not exist because .

Q15:

Given the function , what is true of ?

• AThe limit exists and equals 40.
• BThe limit exists and equals .
• CThe limit does not exist because .

Q16:

Determine .

• A5
• B
• C
• D

Q17:

Given that , determine .

Q18:

Given the function , what is true of ?

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

Q19:

Determine .

• AThe limit does not exist.
• B28
• C29
• D
• E1

Q20:

If , where determine the values of and .

• A,
• B,
• C,
• D,
• E,

Q21:

Determine .

• A
• B
• C
• D26

Q22:

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

• A,
• B,
• C,
• D,