Overview
Here are a few resources for you to review various methods to find limits of functions at infinity. It turns out that apart from a few exceptions, we can apply these methods to sequences as well, by changing the discrete variable \(n\) to a continuous variable \(x\).
You probably have seen most of these methods already in Calculus 1, so use your own judgment on which of the topics you need to review - and when in doubt, you can always start at the beginning, but watch some of the videos at higher speed.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Review various methods to find the limits of functions at infinity.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Be comfortable applying the same methods to find the limits of sequences when applicable.
- Understand how to deal with alternating sequences containing terms of the form \((-1)^n\) (replace these by \(\cos(x\pi)\)).
Basic methods
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Watch the following video (by NancyPi) as needed (to jump to specific topics in this video, click here to watch the video on YouTube, and then use the direct links shown in the description below the video):
L’Hôpital’s Rule
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Read Section 2.8 in Active Calculus as needed.
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Watch the following videos (by GSVUmath):
Conjugates
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Watch this video (by Charles Fortin) to review how to use conjugates for finding certain limits:
Composite functions & powers
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Watch the following video (by Charles Fortin) to see when we can move the limit of a composite function inside the outer function:
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Watch the following video (by Charles Fortin) to see how to apply this technique to determine an indeterminate limit which is a power:
Squeeze Theorem
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Watch the following video (by patrickJMT) on the Squeeze Theorem:
