Chapter 12.5, Problem 48E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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# 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 = x n , x = 1 , n ≥ 2

To determine

To Calculate: The curvature and radius of curvature of plane curve y=xn at x=1 where n2.

Explanation

Given:

The equation of the plane curve y=xn at x=1 where n2..

Formula Used:

The formula for the curvature K of smooth curve C is given by:

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

Calculation:

If C is smooth curve given by y=f(x) then curvature K of C is given by

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

Consider the given equation of plane curve y=xn

Apply the first derivative in the above equation of plane curve and get y'=nxn1.

Apply the second derivative in the above equation of plane curve and get y"=n(n1)xn2.

Apply the formula for the curvature,

K=|n(n1)xn2|[1+(n(x)n1)2

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