# Worksheet: L’Hôpital’s Rule

In this worksheet, we will practice applying L’Hôpital’s rule to evaluate the limits of the indeterminate forms 0/0 and ∞/∞.

Q1:

Find .

• A
• B
• C1
• D10

Q2:

Determine .

Q3:

Determine .

Q4:

Find .

• A
• B
• C
• D

Q5:

Find .

• A
• B
• C
• D

Q6:

Determine .

Q7:

Find .

• A
• B
• C
• D

Q8:

Find .

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

Q9:

Determine .

• A
• B
• C
• D

Q10:

Find .

• A
• B
• C
• D0

Q11:

Find .

• A
• B
• Chas no limit
• D1

Q12:

Find , where

Q13:

Given that , determine the value of .

Q14:

Determine .

• A
• B
• C
• D

Q15:

Determine .

• A
• B16
• C
• D

Q16:

Determine .

• A
• B
• C
• D

Q17:

Find .

• A
• B
• C
• D

Q18:

Determine .

• A
• B
• C
• D

Q19:

Determine .

Q20:

Given functions and , which are positive for large values of , we say that dominates as if

Use l’Hôpital's rule to decide which is dominant as : or .

• A dominates .
• B dominates .

Q21:

Determine .

• A
• B0
• C
• D
• E

Q22:

Find .

• A
• B5
• C
• D
• E

Q23:

Determine

Q24:

Determine .

Q25:

Consider the function .

Determine when .

• A
• B
• C
• D
• E

Where on the number line is ?

• A
• B
• C
• D
• E

What is ?

A sketch of on the interval is a curve below the -axis that is zero at and tends to zero as . Knowing that is differentiable, what would an extended Rolle’s theorem tell us about on the interval ?

• AThe function has a sharp corner at some point .
• BWe cannot get any information about .
• CThe function has a local minimum at some point .
• DThe function is decreasing before some point then starts increasing after that point.
• EThe function has an inflection point at some point , where .