# 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 ∞/∞.

**Q2: **

Determine .

**Q3: **

Determine .

**Q4: **

Find .

- A
- B
- C
- D

**Q5: **

Find .

- A
- B
- C
- D

**Q6: **

Determine .

**Q8: **

Find .

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

**Q9: **

Determine .

- A
- B
- C
- D

**Q10: **

Find .

- A
- B
- C
- D0

**Q11: **

Find .

- A
- B1
- Chas no limit
- D

**Q12: **

Find , where

**Q13: **

Given that , determine the value of .

**Q14: **

Determine .

- A
- B
- C
- D

**Q15: **

Determine .

- A
- B
- C16
- 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
- B
- C
- D0
- E

**Q22: **

Find .

- A
- B
- C
- D
- E5

**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 is decreasing before some point then starts increasing after that point.
- BThe function has an inflection point at some point , where .
- CThe function has a local minimum at some point .
- DWe cannot get any information about .
- EThe function has a sharp corner at some point .