Math 222

Homework #2

Instructions. This is due on January 26 at the beginning of class. It is worth 20 points. Late papers lose 4 points if turned in by 8:00 Monday morning, plus 3 points per additional day late. You must work by yourself, but feel free to consult with me. Explain what you did and why you did it: good explanations are essential! Start early, ask questions and do well.

Problems. In this assignment, you will generate contour plots on Mathematica to help determine whether or not limits exist. Note that contour plots on Mathematica also include shading (unless you turn it off). As with density plots, light areas correspond to large function values and dark areas correspond to small function values. You should use the shading as well as the actual level curves to answer the questions.

Work exploratory exercise 1 on page 949.

Recall the Mathematica syntax:

ContourPlot[x^2/(x^2+y^2),{x,-1,1},{y,-1,1}]