Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises - Page 103: 33

Answer

$\lim\limits_{h\to0}\frac{(x+h)^3-x^3}{h}=3x^2$

Work Step by Step

*Notes: In the question that seemingly contains 2 or more variables, you only need to care about the variable mentioned under $\lim$. $\lim\limits_{h\to0}\frac{(x+h)^3-x^3}{h}$ $=\lim\limits_{h\to0}\frac{(x^3+h^3+3xh^2+3x^2h)-x^3}{h}$ $=\lim\limits_{h\to0}\frac{h^3+3xh^2+3x^2h}{h}$ $=\lim\limits_{h\to0}\frac{h(h^2+3xh+3x^2)}{h}$ $=\lim\limits_{h\to0}(h^2+3xh+3x^2)$ ($h$ gets cancelled) $=0^2+3x\times0+3x^2$ $=3x^2$
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.