Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q. 10 (page 135)

Write the product rule for limits in terms of delta–epsilon statements.

Short Answer

Expert verified

Product rule for limits in terms of delta–epsilon statements |f(x)g(x)-LM|<ε

WhereL=limx→cf(x)andM=limx→cg(x)

Step by step solution

01

Step 1. Given information

Let given limitsf(x)andg(x)

02

Step 2. Write the product rule for limits in terms of delta–epsilon statements. 

The product rule for limit is

limx→c[f(x).g(x)]=limx→cf(x).limx→cg(x)

The strategy is to write the limit expression in delta-epsilon statement

For all ε>0,there exists δ>0such that if 0<|x-c|<δ

Then,

|(f(x)g(x))-(LM)|<ε|f(x)g(x)-LM|<εWhereL=limx→cf(x)andM=limx→cg(x)

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

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

What are punctured intervals, and why do we need to use them when discussing limits?

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

limx→43e1.7x+1

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx→-1x.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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