Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.1 Properties of Functions - 2.1 Exercises - Page 55: 52


a. $x^{2}+2xh+h^{2}-3$ b. $2xh+h^{2}$ c. $2x+h$

Work Step by Step

$f(x)=x^{2}-3$ a. $f(x+h)=(x+h)^{2}-3=(x^{2}+2xh+h^{2})-3$ $=x^{2}+2xh+h^{2}-3$ b. $f(x+h)-f(x)$ $=(x^{2}+2xh+h^{2}-3)-(x^{2}-3)$ $=x^{2}+2xh+h^{2}-3-x^{2}+3$ $=2xh+h^{2}$ c. $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^{2}}{h}=\frac{h(2x+h)}{h}$ $=2x+h$
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