Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q. 92 (page 137)

Prove the difference rule for limits by applying the sum and constant multiple rules for limits.

Short Answer

Expert verified

limx→c(f(x)-g(x))=limx→cf(x)-limx→cg(x)

Step by step solution

01

Step 1. Given Information:

The strategy is to prove the difference rule of limit applying the sum and constant multiple rules for limit.

02

Step 2. Prove:

The difference rule for limit is given by:

limx→c(f(x)-g(x))=limx→cf(x)-limx→cg(x)

Now take the left-hand side we get,

limx→c(f(x)-g(x))=limx→∞[f(x)+(-1)g(x)]=limx→cf(x)+limx→c(-1)g(x)[Sumrule]=limx→cf(x)+(-1)limx→cg(x)[Constantmultiplerule]=limx→cf(x)-limx→cg(x)

Hence, the difference rule can be proved by applying the sum and constant multiple rules.

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.

Start your free trial

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

Most popular questions from this chapter

limx→+22x-4

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→0(x3+1)=1

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→-2(4-2x)=8

Write delta-epsilon proofs for each of the limit statements limx→cfx=Lin Exercises 47-60.

limx→46x-1=23.

Use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.
Ifx>N, then1−2x<−500
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

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.

Sign-up for free