Question

Asked Feb 25, 2019

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

(a) 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.

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

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

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Step 1

To analyze the function z=f(x,y)=y sin(1/x) (x not 0)

Step 2

(a) the level curves for x=0 consists of the x-axis and the series of lines x=1/(n*pi), n any non-zero integer.

Step 3

Level curves for c=0. Note that there are infinitely many ...

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