LIMITS, brief review:

Recall (convince yourself if necessary, or review chapter 2 in the text):

1.

2. In the case of a limit of a fraction of polynomials, you can reduce the limit to the above situations by dividing both the top and the bottom by the largest power of the variable. For example:

3. Review limits at 0, and any other asymptotes for the usual functions:

4. Review textbook section 4.4 on Indeterminate Limits and L’Hospital

Common types of indeterminate limits:

(Can apply L’Hospital)
(First simplify or reduce it to a L’Hospital type of limit)

L’Hospital’s Rule: If you have an indeterminate limit of one of the types: and if the functions satisfy certain conditions around the limit point (see page 308 in textbook) then

Example: