Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises - Page 103: 17



Work Step by Step

To take the derivative of a function using the limit process, plug into the equation $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$ and simplify: $f'(x)=\lim\limits_{h \to 0}\frac{[(x+h)^{2}+(x+h)-3]-(x^2+x-3)}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{x^2+2xh+h^2+x+h-3-x^2-x+3}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{2xh+h^2+h}{h}$ $f'(x)=\lim\limits_{h \to 0}2x+h+1$ Once you can't simplify any further, plug 0 in for $h$: $f'(x)=2x+(0)+1=2x+1$
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