Calculus 8th Edition

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

Chapter 1 - Functions and Limits - Review - Exercises: 34

Answer

$\dfrac {-5}{54}$

Work Step by Step

$\lim _{x\rightarrow 3}\dfrac {\sqrt {x+6}-x}{x^{3}-3x^{2}}=\dfrac {\left( \sqrt {x+6}-x\right) \left( \sqrt {x+6}+x\right) }{x^{2}\left( x-3\right) \left( \sqrt {x+6}+x\right) }=\dfrac {x+6-x^{2}}{x^{2}\left( x-3\right) \left( \sqrt {x+6}+x\right) }=\dfrac {-\left( x-3\right) \left( x+2\right) }{x^{2}\left( x-3\right) \left( \sqrt {x+6}+x\right) }=-\dfrac {x+2}{x^{2}\left( \sqrt {x+6}+x\right) }=\dfrac {-5}{54}$
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.