Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.4 - Introduction to Derrivatives - Exercise Set - Page 1174: 11


a) $\dfrac{1}{6}$ b) $ y=\dfrac{1}{6}x+\dfrac{3}{2}$

Work Step by Step

a) Now, $ m_{\tan}=\lim_\limits{ h\to 0} \dfrac{f(9+h)-f(9)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\sqrt{9+h}-\sqrt 9}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{1}{\sqrt {9+h}+3}$ At $(9,3)$; $ m_{\tan}=\dfrac{1}{6}$ b) The equation of a line is: $ y=mx+c $ Now, $ y-3=(1/6)(x-9) \implies y=\dfrac{1}{6}x+\dfrac{3}{2}$
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