Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise: 10

Answer

limits does not exist.

Work Step by Step

We notice that if we directly substitute limits in the given function $f(x,y)=\frac{5y^{4}cos^{2}x}{x^{4}+y^{4}}$ Then $f(0,0)=\frac{0}{0}$ Therefore, we will calculate limit of function in following way. To evaluate the limit along x-axis; put $y=0$ $f(x,0)=\frac{5y^{4}cos^{2}x}{x^{4}+y^{4}}=\frac{5(0)^{4}cos^{2}x}{x^{4}+0}=0$ To evaluate limit along y-axis; put $x=0$ $f(0,y)=\frac{5y^{4}cos^{2}x}{x^{4}+y^{4}}=5$ For a limit to exist, all the paths must converge to the same point. Hence, both the limits are different and follow different paths, thus, the given limit does not exist.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.