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Question

Let f(x, y) = y sin(1/x).

(a) What is the domain of f?

I think it's all values of (x,y) where x is not 0

(b) What is the range of f; that is, which values does f(x, y) take for (x, y) in its domain?

I think it's all real numbers

(c) Determine the limit lim (x,y)→(0,0) y sin(1/x) and explain your answer.

(d) For c = 0 and c = 1, write an equation for the level curve f(x, y) = c, and draw them in the region where −2 ≤ x ≤ 2 and −2 ≤ y ≤ 2. Please use two different colors to indicate the two level curves, and feel free to use a graphing calculator to help you!

(e) Explain why lim (x,y)→(0,1) y sin(1/x) does not exist.

(f) From the surfaces drawn on the back of this page, determine the graph of f. (I attached as an image)

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