Calculus (3rd Edition)

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

Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 4


$$\left\langle 1 ,1 ,0\right\rangle $$

Work Step by Step

By making use of L'Hôpital's rule on the second component, we have $$ \lim _{t \rightarrow 0} \left\langle \frac{1}{t+1} , \frac{e^t-1}{t} ,4t\right\rangle=\\ \left\langle\lim _{t \rightarrow 0}\frac{1}{t+1} ,\lim _{t \rightarrow 0} \frac{e^t-1}{t} ,\lim _{t \rightarrow 0}4t\right\rangle\\ =\left\langle 1 ,1 ,0\right\rangle $$
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.