Section 15.2 Worksheet:

Assigned problems: Exercises Page 928: 1-3, 5, 7, 10, 15, 21, 27, 29, 35, 37 (due Monday, 1/26).

1. What are the typical problems for limits and continuity in the univariate case? Give examples of functions f and points a for which
   • doesn't exist

   • exists, but the function isn't continuous

   • has limits and is continuous.

2. How is the process of establishing limits different between univariate and multivariate functions?

3. Where are rational multivariate functions continuous?

4. Can the limit exist at a point but the function fail to be continuous there? Can the function be continuous at a point but the limit fail to exist at the point?

5. How can contours help us to analyze limits and continuity in the bivariate case?