Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
1 views

Finding Curvature In Exercises 29-36, find the curvature of the curve. r ( t ) = e 2 t i + e 2 t cos t j + e 3 t sin t k

To determine

To Calculate: The curvature of the curve having position vector r(t)=e2ti+e2tcostj+e2tsintk.

Explanation

Given:

The curve r(t)=e2ti+e2tcostj+e2tsintk.

Formula Used:

The curvature for the curve r(t) is given by: n=||T(t)||||r(t)||

Where; T(t)=r'(t)||r'(t)||.

Calculation:

It is not apparent whether this parameter represents arc length, so use the formula

n=||T(t)||||r(t)||

Here, r'(t)=2e2ti^+(2e2tcoste2tsint)j^+(2e2tsint+e2tcost)k^

Find the norm of position vector r(t)

||r(t)||=4e4t+4e4tcos2t+e4tsin2t+4e4tsin2t+e4tcos2t=4e4t+4e4t+e4t=3e2t

Find the unit tangent vector T

T(t

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