Calculus: Early Transcendentals (2nd Edition)

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

Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises: 30


$\langle \frac{\sqrt 7}{5},\frac{3}{5},\frac{3}{5}\rangle $

Work Step by Step

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle \sqrt 7e^t,3e^t,3e^t\rangle$ $\textbf{r}'(t) = \langle \sqrt 7e^t,3e^t,3e^t\rangle$ $|\textbf{r}'(t)| = \sqrt {(\sqrt 7e^t)^2 + (3e^t)^2 + (3e^t)^2} = \sqrt {25e^{2t}}$ $\textbf{T}(t) = \frac{\textbf{r}'(t)}{|\textbf{r}'(t)|} = \frac{\langle \sqrt 7e^t,3e^t,3e^t\rangle}{ \sqrt {25e^{2t}}} = 5e^t$ $\textbf{T}(ln(2)) = \frac{\langle \sqrt 7e^{ln(2)},3e^{ln(2)},3e^{ln(2)}\rangle}{ 5e^{ln(2)}} = \langle \frac{\sqrt 7}{5},\frac{3}{5},\frac{3}{5}\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.