/*! 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. 52 For each limit limx鈫抍f(x)=Lin ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 52 (page 97)

For each limit limx鈫�cf(x)=Lin Exercises 43鈥�54, use graphs and algebra to approximate the largest value of 未such that if x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚).

limx鈫�32-x2=-7,蔚=0.001

Short Answer

Expert verified

The largest value of未=0.0001666.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�32-x2=-7,蔚=0.001.

02

Step 2. Explanation. 

From the given expression, we have,c=3,L=-7.

The limit expression can be written as a formal statement as below,

For all epsilon positive, there exists a delta positive such that if

role="math" localid="1648189035483" x鈭�(3-未,3)鈭�(3,3+未)then2-x2鈭�(-7-蔚,-7+蔚)

Now, the largest value of delta is given by,

2-x2=L+蔚2-x2=-7-0.0012-x2=-7.0012+7.001=x29.001=x2x=9.001

Thus,

未=9.001-3未鈮�0.0001666

03

Step 3. Conclusion.

The largest value of未鈮�0.0001666.

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�02xex-1

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�21x=12;youmayassume未鈮�1

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

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)=x鈭�1/2

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

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.