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 - Page 56: 17



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 and the product rule for limits, we have $\lim\limits_{x \to -\frac{1}{2}}4x(3x+4)^2=4(-\frac{1}{2})(3(-\frac{1}{2})+4)^2=-2(-\frac{3}{2}+4)^2=-2(-\frac{3}{2}+\frac{8}{2})^2=-2(\frac{5}{2})^2=-2(\frac{25}{4})=-\frac{25}{2}.$
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