Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.3 Basic Limit Laws - Exercises - Page 59: 20



Work Step by Step

$\lim\limits_{t \to -1}\frac{t^{2}+1}{(t^{3}+2)(t^{4}+1)}=\frac{\lim\limits_{t \to -1}(t^{2}+1)}{\lim\limits_{t \to -1}[(t^{3}+2)(t^{4}+1)]}$ (Quotient Law) $=\frac{\lim\limits_{t \to -1}(t^{2}+1)}{(\lim\limits_{t \to -1}t^{3}+2)(\lim\limits_{t \to -1}t^{4}+1)}$ (Product Law) $=\frac{\lim\limits_{t \to -1}t^{2}+\lim\limits_{t \to -1}1}{(\lim\limits_{t \to -1}t^{3}+\lim\limits_{t \to -1}2)(\lim\limits_{t \to -1}t^{4}+\lim\limits_{t \to -1}1)}$ (Sum Law) $=\frac{1+1}{(-1+2)(1+1)}=1$
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