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".
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at our 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 \(\cos(x\pi)\)).
Read Section 2.8 in the textbook as needed.
Watch the following videos:
Watch this video to review how to use conjugates for finding certain limits:
Composite functions & powers
Watch the following video to see when we can move the limit of a composite function inside the outer function:
Watch the following video to see how to apply this technique to determine an indeterminate limit which is a power:
Watch the following video on the Squeeze Theorem: