Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.1 - Functions from the Numerical, Algebraic, and Graphical Viewpoints - Exercises - Page 53: 40


a. $\quad h(2x+1+h)$ b. $\quad 2x+1+h$

Work Step by Step

a. $ f(x+h)=(x+h)^{2}+(x+h)=\quad$ ...square of a sum $=x^{2}+2xh+h^{2}+x+h$ $f(x+h)-f(x)=x^{2}+2xh+h^{2}+x+h-(x^{2}+x)$ $=x^{2}+2xh+h^{2}+x+h-x^{2}-x$ $=2xh+h+h^{2}$ $=h(2x+1+h)$ b. using the result of (a), $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{h(2x+1+h)}{h}=\quad$ .. reduce h, $=2x+1+h$
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