   Chapter 13, Problem 6RCC

Chapter
Section
Textbook Problem

# (a) What is the definition of curvature?(b) Write a formula for curvature in terms of r'(t) and T'(t).(c) Write a formula for curvature in terms of r'(t) and r"(t).(d) Write a formula for     the curvature of a plane curve with equation y = f(x).

(a)

To determine

To define: The curvature.

Explanation

The curvature of a curve (k) is,

k=|dTds|, where T is the unit tangent vector

(b)

To determine

To find: A formula for curvature in terms of r(t) and T(t).

(c)

To determine

To find: A formula for curvature in terms of r(t) and r(t).

(d)

To determine

To find: A formula for curvature of a plane with equation y=f(x).

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