Chapter 12.5, Problem 22E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
1 views

# 57095-12.5-22E-Question-Digital.docxFinding Curvature In Exercises 19–22, find the curvature K of the curve, where s is thearc length parameter.Curve in Exercise 18: r ( t ) = 〈 4 ( sin   t − t   cos   t ) , 4 ( cos   t + t   sin   t ) , 3 2 t 2 〉

To determine

To calculate: The curvature of the curve r(t)=4(sinttcost),4(cost+tsint),32t2.

Explanation

Given:

The equation of curve r(t)=4(sinttcost),4(cost+tsint),32t2.

Formula used:

The curvature of curve r(t) is,

K=T(t)r(t)

Calculation:

Consider the equation of the curve, r(t)=4(sinttcost),4(cost+tsint),32t2.

Differentiate r(t) with respect to t,

r(t)=4(cost(costtsint) i)+4(sint+(sint+tcost))j+ 3t k

Take the magnitude of r(t), That is,

r(t)=42(cost(costtsint) i)2+42(sint+(sint+tcost)j)2+ (3t k)2=16(tsint)2+(tcost)2+(3t)2=16t2(sin2t+cos2t)+9t2=16t2+9t2

Further simplify the above equation,

r(t)=25t2=5t

Find the value of tangent vector,

T

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started