# 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.

**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 is smaller 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 greater than that of as .
- EThe growth rate of becomes 0, while the growth rate of becomes as .

**Q3: **

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

**Q4: **

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

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

**Q5: **

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 , while the growth rate of becomes 0 as .
- DThe growth rate of is smaller than the growth rate of .
- EThe growth rate of becomes 0, while the growth rate of becomes as .

**Q7: **

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

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

**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 equal to the growth rate of .
- EThe growth rate of is greater than the growth rate of .

**Q9: **

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

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

**Q10: **

Consider the functions and .

Evaluate using lβHΓ΄pitalβs rule.

Evaluate using lβHΓ΄pitalβs rule.

- A
- B2
- C0
- DThe limit does not exist.
- E1

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

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

**Q11: **

Given that and , use to determine whether or is dominant.

- A is the dominant function.
- BNeither nor is the dominant function.
- C is the dominant function.

**Q15: **

Given that and , use to determine whether or is dominant.

- ANeither nor is the dominant function.
- B is the dominant function.
- C is the dominant function.