## Calculus 8th Edition

Published by Cengage

# Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises: 47

#### Answer

$-\infty$

#### 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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