Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 24

Answer

$-\infty$

Work Step by Step

Find the limit $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)$ This is quadratic equation in the powers of 2 with roots $(x-2)$$(x-3)$. $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=\lim\limits_{x \to 3^{+}}log_{10}(x-2)(x-3)$ The limit of the logarithm base 10 of $x$ when $x$ approaches zero from the positive side (0+) is minus infinity. This implies $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=-\infty$
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