Chapter 12, Problem 70RE

### 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 Rectangular Coordinates In Exercises 69-72, find the curvature and radius of curvature of the plane curve at the given value of x. y = tan x , x = π 4

To determine

To calculate: The curvature and radius of curvature of the plane curve y=tanx at x=π4.

Explanation

Given:

The function of plane curve is: y=tanx at x=π4.

Formula used:

The curvature of the plane is calculated as:

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

Calculation:

Consider the function:

y=tanx

Differentiate and then again differentiate y to obtain:

y=sec2x and y=2sec2xtanx

Substitute x=π4 and obtain:

yx

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