Homework for Sept 21:
Consider the function
f (x, y) =
xy 2
.
+ y4
x2
1. What is the domain of f ?
2. Find limt→0 f (t, ct), when c is a constant.
3. For each n > 0, the point (xn , yn ) given by x = 1/n2 , y = 1/n lies on the
line y = nx. Find f (xn , yn ) for n = 1, n = 2, and n = 3. Do you see a
pattern?
4. True or false: “The limit as (x, y) goes to (0, 0) of f (x, y) is 0.” Explain.
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