Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises - Page 446: 15



Work Step by Step

Find the limit $\lim\limits_{x \to 3^{+}}ln(x^{2}-9)$ This is quadratic equation in the powers of 2. Suppose, $n=\lim\limits_{x \to 3^{+}}(x^{2}-9)$ $=\lim\limits_{x \to 3^{+}}(x-3)(x+3)$ Thus, $n=0$ The limit of the natural logarithm of $x$ when $x$ approaches zero from the positive side (0+) is minus infinity. This implies Hence, $\lim\limits_{x \to 3^{+}}ln(x^{2}-9)=-\infty$
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