Calculus 8th Edition

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

Chapter 1 - Functions and Limits - Review - Exercises: 33

Answer

$\dfrac {4}{7}$

Work Step by Step

$\lim _{u\rightarrow 1}\dfrac {u^{4}-1}{u^{3}+5u^{2}-6u}=\dfrac {\left( u^{2}-1\right) \left( u^{2}+1\right) }{u\left( u^{2}+5u-6\right) }=\dfrac {\left( u-1\right) \left( u+1\right) \left( u^{2}+1\right) }{u\left( u-1\right) \left( u+6\right) }=\dfrac {\left( u+1\right) \left( u^{2}+1\right) }{u\left( u+6\right) }=\dfrac {4}{7}$
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