Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 29

Answer

$-\infty$

Work Step by Step

We have $$ \lim _{x \rightarrow 3^+} \frac{x-4}{x^2-9}=\lim _{x \rightarrow 3^+} \frac{x-4}{(x+3)(x-3)}=- \infty. $$ We know that the limit from the right will be negative infinity because the numerator will be negative (since 3 is less than 4), while the denominator will be positive. The denominator will be arbitrarily close to zero, producing an infinite result.
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