Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Write a delta–epsilon proof that proves that fis continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.

f(x)=x1/2

Short Answer

Expert verified

Ans: f(x)=x12is continuous on its domain (continuous for all xR)

Step by step solution

01

Step 1. Given information.

Given, f(x)=x1/2

02

Step 2. Domain: 

Since, xis defined fo all xR

03

Step 3. So, check for continuity.  

Let cbe any real number.

fis continuous atx=c

assume thatc is less than or equal to1

x=cif, role="math" localid="1648053742246" limxcf(x)=f(c)

LHS=limxcf(x)=limxcxPuttingx=c=c

RHS=f(c)=c


04

Step 4.  Since, LHS=RHS

So, Function is continuous at x=c

Thus, we can write that

f(x)=x12continuous for allxR.

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 Vaia!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free