Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2: 21



Work Step by Step

We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this along with the quotient, sum, and root rules for limits, we have $\lim\limits_{h \to 0}\dfrac{3}{\sqrt{3h+1}+1}=\dfrac{3}{\sqrt{3(0)+1}+1}=\dfrac{3}{\sqrt{0+1}+1}=\dfrac{3}{\sqrt{1}+1}=\dfrac{3}{1+1}=\dfrac{3}{2}.$
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