MATH237 Study Guide - Quiz Guide: Squeeze Theorem
20 Jun 2019
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237s0ls16: since x2 + y2 6= 0 if (x, y) 6= (0, 0), we have that f is continuous for all (x, y) 6= (0, 0) by the continuity theorems. For f to be continuous at (0, 0) we must have lim (x,y) (0,0) f (x, y) = 0. We try to prove this with the squeeze theorem. We have x4 y4 (cid:12) (cid:12) x2 + y2 0 (cid:12) (cid:12) since x2 x2 + y2 and y2 x2 + y2. Thus, since lim(x,y) (0,0) x2 + y2 = 0, we get f (x, y) = 0 by the squeeze theorem. Note that this will probably not work on mobile devices such as ipads, but it will definitely work on mac and windows computers, both personal and in the mfcf labs. Page 2 of 2: a) f is continuous for all (x, y) 6= (0, 0) by the continuity theorems.
