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)

2
2
2
0
2
4202
21012
2
2
0
2
2
2
05050
100
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2 2 2 0 2 4202 21012 2 2 0 2 2 2 05050 100

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Expert Answer

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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. 

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Step 3

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

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Math

Calculus