Claire H.

asked • 12/28/16

Finding critical points and limits.

Let f(x,y) = 1/(x2 - y)
(a) Determine the critical points of f.
(b) Does the limit of the function f at the point (0, 0) exist? Justify your answer

1 Expert Answer

By:

Stephen M. answered • 12/28/16

Naval Academy Grad for Math and Science Tutoring

Claire H.

Ah I see, I think. So in part (b), as I approach the origin along the y axis (or x = 0) the function approaches negative infinity, while if I approach it from the x - axis (or y = 0) the function tends towards positive infinity. Hence, the limit does not exist??
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12/28/16

Stephen M.

tutor
Exactly.  Although each axis can be approached from either direction.  So for the y axis (x=0), we get a negative approaching from y>0 and a positive approaching from y<0.    But yes, it's also positive along the x-axis y=0 (in both directions).
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12/28/16

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