# Worksheet: Comparing Rate of Growth of Functions

In this worksheet, we will practice using limits to compare the relative magnitudes of functions and their rates of change.

**Q1: **

For the functions and , evaluate using lβHΓ΄pitalβs rule.

**Q2: **

Evaluate using lβHΓ΄pitalβs rule.

From the answer to the limit, what can you say about the growth rate of compared to as ?

- AThe growth rate of becomes , while the growth rate of becomes 0 as .
- BThe growth rate of is greater than that of as .
- CThe growth rate of becomes 0, while the growth rate of becomes as .
- DThe growth rate of is equal to that of as .
- EThe growth rate of is smaller than that of as .

**Q3: **

If , what do you notice about the growth rate of compared to as ?

- AThe growth rate of becomes , while the growth rate of becomes 0 as .
- BThe growth rate of is equal to that of as .
- CThe growth rate of is greater than that of as .
- DThe growth rate of becomes 0, while the growth rate of becomes as .
- EThe growth rate of is smaller than that of as .

**Q4: **

If , what do you notice about the growth rate of compared to as ?

- AThe growth rate of is greater than that of as .
- BThe growth rate of becomes , while the growth rate of becomes 0 as .
- CThe growth rate of is equal to that of as .
- DThe growth rate of is smaller than that of as .
- EThe growth rate of becomes 0, while the growth rate of becomes as .

**Q5: **

Compare the growth rate of the two functions and using limits as .

- AThe growth rate of is smaller than the growth rate of .
- BThe growth rate of becomes , while the growth rate of becomes 0 as .
- CThe growth rate of is greater than the growth rate of .
- DThe growth rate of becomes 0, while the growth rate of becomes as .
- EThe growth rate of is equal to the growth rate of .

**Q6: **

For the functions and , evaluate using lβHΓ΄pitalβs rule.

**Q7: **

Compare the growth rate of the two functions and using limits as .

- AThe growth rate of becomes 0, while the growth rate of becomes as .
- BThe growth rate of is equal to the growth rate of .
- CThe growth rate of is greater than the growth rate of .
- DThe growth rate of becomes 0, while the growth rate of becomes as .
- EThe growth rate of is greater than the growth rate of .

**Q8: **

Compare the growth rate of the two functions and using limits as .

- AThe growth rate of becomes 0, while the growth rate of becomes as .
- BThe growth rate of is greater than the growth rate of .
- CThe growth rate of becomes 0, while the growth rate of becomes as .
- DThe growth rate of is greater than the growth rate of .
- EThe growth rate of is equal to the growth rate of .

**Q9: **

Compare the growth rate of the two functions and using limits as .

- AThe growth rate of is equal to the growth rate of .
- BThe growth rate of is greater than the growth rate of .
- CThe growth rate of becomes 0, while the growth rate of becomes as .
- DThe growth rate of is smaller than the growth rate of .
- EThe growth rate of becomes , while the growth rate of becomes 0 as .

**Q10: **

Consider the functions and .

Evaluate using lβHΓ΄pitalβs rule.

Evaluate using lβHΓ΄pitalβs rule.

- A1
- B0
- C
- D2
- EThe limit does not exist.

What do you get from the two results about the growth rates of and as ?

- AThe growth rate of is greater than that of as .
- BThe growth rate is the same for both as .
- CThe growth rate of becomes 0, while the growth rate of becomes as .
- DThe growth rate of becomes 0, while the growth rate of becomes as .
- EThe growth rate of is greater than that of as .