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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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57095-12.5-46E-Question-Digital.docx

Finding Curvature in Rectangular Coordinates In Exercises 41–48, find the curvature and radius of curvature of the plane curve at the given value of x.

y = e 3 x , x = 0

To determine

To calculate: The curvature and radius of curvature of plane curve y=e3x at x=0.

Explanation

Given:

The equation of plane curve, y=e3x and value of x is 0.

Formula:

The curvature (K) of plane curve is,y=f(x) is,

K=|y|[1+(y)2]32

The formula for radius of curvature,

r=1K

Where r is the radius of the curve y=f(x).

Calculation:

Consider the equation of the curve y=e3x.

Differentiate above equation with respect to x,

y(x)=3e3x

Again, differentiate above equation with respect to x,

y(x)=3e3x(3)=9e3x

Substitute the value of y(x) and y(x) in the formula for the curvature,

K=|y|[1+(y)2]32=|9e3x|[

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