University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Practice Exercises - Page 111: 31



Work Step by Step

$$\lim_{x\to1}\frac{3x^2+1}{g(x)}=\infty$$ $$\frac{\lim_{x\to1}(3x^2+1)}{\lim_{x\to1}g(x)}=\infty$$ $$\frac{3\times1^2+1}{\lim_{x\to1}g(x)}=\infty$$ $$\frac{4}{\lim_{x\to1}g(x)}=\infty$$ For $\frac{4}{\lim_{x\to1}g(x)}$ to reach infinity, $\lim_{x\to1}g(x)$ needs to be equal to $0$. $$\lim_{x\to1}g(x)=0$$
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