Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 42


$\infty $

Work Step by Step

Given $$\lim_{x\to-5^-} \frac{3x}{2x+10}$$ When $ x $ approaches $-5$ from the left, then $2 x+10<0,$ so the denominator approaches 0 from the left side. $ L=\frac{\rightarrow-15}{\rightarrow 0^{-}}=\infty $ This is because if the numerator approaches a negative number and the denominator approaches 0 from the left side, the result is $\infty $ .
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