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 - Practice Exercises - Page 100: 3


a. $-21$ b. $49$ c. $0$ d. $1$ e. $1$ f. $7$ g. $-7$ h. $-\frac{1}{7}$

Work Step by Step

Given $\lim_{t\to t_0}f(t)=-7$ and $\lim_{t\to t_0}g(t)=0$ a. $\lim_{t\to t_0}3f(t)=3\lim_{t\to t_0}f(t)=3\times(-7)=-21$ b. $\lim_{t\to t_0}(f(t))^2=(-7)^2=49$ c. $\lim_{t\to t_0}f(t)g(t)=-7\times0=0$ d. $\lim_{t\to t_0}\frac{f(t)}{g(t)-7}=\frac{-7}{0-7}=1$ e. $\lim_{t\to t_0}cos(g(t))=cos0=1$ f. $\lim_{t\to t_0}|f(t)|=|-7|=7$ g. $\lim_{t\to t_0}(f(t)+g(t))=-7+0=-7$ h. $\lim_{t\to t_0}\frac{1}{f(t)}=-\frac{1}{7}$
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