/*! 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. 38 For each limit statement , use a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 38 (page 107)

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�31x=13;youmayassume未鈮�1

Short Answer

Expert verified

未=min(1,3蔚)

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�31x=13;youmayassume未鈮�1.

We have to find 未intermsof蔚.

02

Step 2. Use algebra.

From the given limit statement, we can identify

f(x)=1xc=3L=13For蔚>01x鈭�13<蔚3鈭�x3x<蔚13|x鈭�3|<蔚|x鈭�3|<3蔚For0<|x鈭�c|<未,weget|x鈭�3|<3蔚.Therefore,未=min(1,3蔚)

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

limx鈫�0ex-1e2x+2ex-3

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

f(x)=x3

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�-2(4-2x)=8

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�2(x2-4x+6)=2

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

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.