Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 951: 39



Work Step by Step

Conversion of polar co-ordinates $(r, \theta)$ are: $x=r \cos \theta$ and $y= r \sin \theta$ Given: $\lim\limits_{(x,y) \to(0,0)}\dfrac{x^3+y^3}{x^2+y^2}$ This implies $=\lim\limits_{r \to0}\dfrac{(r \cos \theta)^3+(r \sin \theta)^3}{(r \cos \theta)^2+(r \sin \theta)^2}$ $=\lim\limits_{r \to 0}\dfrac{r^3( \cos^3 \theta+ \sin ^3\theta)}{r^2( \cos ^2\theta+ \sin^2 \theta)}$ $=\lim\limits_{r \to 0} r(\cos \theta +\sin \theta)$ $=0$
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