Question

Find the curvature of the curve defined by ?r(t) = e^{4t}?i + 5t?j K = Evaluate the curvature at the point P(2980.958, 10). Note: You may want to enter very small or very large curvatures in scientific notation.

          Find the curvature of the curve defined by

?r(t) = e^{4t}?i + 5t?j

K =

Evaluate the curvature at the point P(2980.958, 10).

Note: You may want to enter very small or very large curvatures in scientific notation.

Added by Hailey J.

Calculus Early Transcendental Functions

Ron Larson, Bruce Edwards 6th Edition

Chapter 12

Instant Answer

Solved by Expert Zhumagali Shomanov

06/23/2023

Step 1

The given position vector is: \[ \vec{r}(t) = e^{4t\vec{i} + 5t\vec{j}} \] First, we need to find the first derivative of the position vector with respect to t: \[ \vec{r'}(t) = \frac{d\vec{r}(t)}{dt} \] Using the chain rule, we get: \[ \vec{r'}(t) = Show more…

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