/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 60 Use Theorem 11.24 to prove that ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q. 60 (page 890)

Use Theorem 11.24 to prove that the curvature of a linear function y = mx + b is zero for every value of x.

Short Answer

Expert verified

It is proved thatthe curvature of a linear functiony = mx + b is zero for every value ofx.

Step by step solution

01

Step 1. Given Information.

The given linear function isy=mx+b.

02

Step 2. Prove.

To prove that the curvature of a linear function y = mx + b is zero for every value of x,we will use the formula for Curvature in the Plane.

The curvature in the plane is defined as letting y = f(x) be a twice-differentiable function. Then the curvature of the graph of fis given by k=f''(x)1+f'x232.

Now,

y=f(x)=mx+bf'x=mf''x=0

Put all the values in the formula,

k=01+m232k=0

Hence proved.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If 伪, 尾, and 纬are nonzero constants, the graph of a vector function of the formrole="math" localid="1649577570077" rt=伪t,尾t2,纬t3 is called a twisted cubic. Prove that a twisted cubic intersects any plane in at most three points.

Evaluate and simplify the indicated quantities in Exercises 35鈥�41.

(1,t,t2)脳(1,t2,t3)

In Exercises 19鈥�21 sketch the graph of a vector-valued function r(t)=x(t),y(t) with the specified properties. Be sure to indicate the direction of increasing values oft.

Domainlocalid="1649578783745" t鈮�0,r0=1,0,r2=0,-1,limt鈫�鈭�x(t)=-2,andlimt鈫�鈭�y(t)=-3.

Lett=f(蟿)beadifferentiablereal-valuedfunctionof蟿,andletr(t)beadifferentiablevectorfunctionwitheithertwoorthreecomponentssuchthatf(蟿)isinthedomainofrforeveryvalueof蟿onsomeintervalI.Finddrf蟿d蟿.

Let r(t) be a differentiable vector function. Prove that role="math" localid="1649602115972" ddt鈥�r鈥�=1鈥�r鈥�r路rr路 (Hint: role="math" localid="1649602160237" 鈥�r鈥�2=r路r
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.