Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.3 Techniques for Computing Limits - 2.3 Exercises - Page 76: 4

Answer

$4$

Work Step by Step

$f$ is defined for all $x$ near $a$ with $x\lt a,$ as $f(x)=g(x).$ Then, $\displaystyle \lim_{x\rightarrow 3^{-}}f(x)=\lim_{x\rightarrow 3^{-}}g(x)=4,$ because the left-sided limit of g exists, and equals the limit of g(x) at 3. $f$ is defined for all $x$ near $a$ with $x\gt a,$ as $f(x)=g(x).$ Then, $\displaystyle \lim_{x\rightarrow 3^{+}}f(x)=\lim_{x\rightarrow 3^{+}}g(x)=4,$ because the right-sided limit of g exists, and equals the limit of g(x) at 3. We have now, at x=3, both the one-sided limits of f(x) exist and are equal to 4. Then, the limit of f at x=3 exists and $\displaystyle \lim_{x\rightarrow 3}f(x)=4$
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.