   Chapter 13.3, Problem 43E

Chapter
Section
Textbook Problem

# Use the formula in Exercise 42 to find the curvature.43. x = t2, y = t3

To determine

To find: The curvature of plane with parametric equations x=t2 and y=t3.

Explanation

Given:

The Parametric equations are x=t2 and y=t3.

Formula used:

The curvature of plane k(t) with parametric equation x=f(t), y=g(t) is,

k(t)=|x˙y¨x¨y˙|(x˙2+y˙2)32 (1)

Consider the given equation.

x=t2

Differentiate the equation with respect to t.

x˙=ddt(t2)=2t {ddx(x2)=2x}

Find the value of x¨.

x¨=ddt(2t)=2(1) {ddx(x)=1}=2

Consider the given equation.

y=t3

Find the value of y˙.

y˙=ddt(t3)=3t2 {ddx(xn)=nxn1}

Find the value of y¨

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