Calculus (3rd Edition)

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

Chapter 2 - Limits - Chapter Review Exercises - Page 94: 22



Work Step by Step

We evaluate the limit: \begin{aligned} \lim_{y\to 1/3}\frac{3 y^{2}+5 y-2}{6 y^{2}-5 y+1} &=\lim_{y\to 1/3}\frac{3 y^{2}-y+6 y-2}{6 y^{2}-2 y-3 y+1} \\ &=\lim_{y\to 1/3}\frac{y(3 y-1)+2(3 y-1)}{2 y(3 y-1)-(3 y-1)} \\ &=\lim_{y\to 1/3}\frac{(3 y-1)(y+2)}{(3 y-1)(2 y-1)}\\ &=\lim_{y\to 1/3}\frac{y+2}{2 y-1}\\ &= \frac{7/3}{-1/3}=-7 \end{aligned}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.