MATH 20C Lecture 14

14.2 Limits and Continuity

How to find limits

Method 1

If is continuous at , then

Method 2

Let As
L’Hospital’s Rule
If is of the form or then

Method 3: Squeeze Theorem

Note

Since
By the squeeze theorem

Method 4: Showing that a limit does not exist (DNE)

Find the limit approaching along the x axis and along the y axis. Show that they are not equal.

Method 5

Does the limit exist?


This shows that the limit along all lines are the same. But this does not prove that exists.


depends on .
DNE

Method 6: Polar coordinates

are the polar coordinates.
.
For any path to , we can consider as a function of near