/*! 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. 71 Prove each of the limit statemen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 71 (page 108)

Prove each of the limit statements in Exercises67鈥�72. You

will have to bound 未.

limx鈫�24x2=1

Short Answer

Expert verified

The given limit limx鈫�24x2=1is proved.

Step by step solution

01

Step 1. Given information. 

We are given,

limx鈫�24x2=1

02

Step 2. Proving the limit 

Given 蔚>0, choose 未=min1,蔚3.

Then if 0<|x-2|<未, we have,

4x2-1=4-x2x2=|(2-x)(2+x)|x2=|x-2||x+2|x2<未|x+2|x2鈮�未(3)鈮�蔚33=蔚

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

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

limx鈫�2x2-3x+2x-2=1

Calculate each of the limits:

limx鈫�1xsin-1x2.

For each limit statement in Exercises 41-44, use algebra to find 未or Nin terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�x-1x=1, findNin terms of蔚.

State what it means for a function f to be left continuous at a point x = c, in terms of the delta鈥揺psilon definition of limit.

Find a formula for the cost Crof producing a gourmet soup can with radius rand height 5inches, and answer the following questions:

  1. What is the radius of a can that is 5inches tall and costs 30cents to produce?
  2. Your manager wants you to produce 5-inch-tall cans that cost between 20and 40cents. Write this requirement as an absolute value inequality.
  3. What range of radii would satisfy your manager? Write an absolute value inequality whose solution set lies inside this range of radii.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.