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In this lesson, we will learn how to use limits to compare the relative magnitudes of functions and their rates of change.
Q1:
For the functions π(π₯)=2π₯ο¨ and π(π₯)=4πο¨ο, evaluate limοββο½π(π₯)π(π₯)ο using lβHΓ΄pitalβs rule.
Q2:
Evaluate limοββο¨οοΎπ₯πο using lβHΓ΄pitalβs rule.
From the answer to the limit, what can you say about the growth rate of π₯ο¨ compared to πο as π₯ββ?
Q3:
If limοββο½π(π₯)π(π₯)ο=0, what do you notice about the growth rate of π(π₯) compared to π(π₯) as π₯ββ?
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