/*! 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. 50 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. 50 (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�01-cosxx=0,蔚=14

Short Answer

Expert verified

The largest value of未鈮�0.511.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�01-cosxx=0,蔚=14.

02

Step 2. Explanation. 

From the given expression, we have,c=0,L=0

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

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

x鈭�(0-未,0)鈭�(0,0+未)then1-cosxx鈭�(0-蔚,0+蔚)

Now, the largest value of delta is given by,

1-cosxx=L+蔚1-cosxx=0+141-cosxx=14x=4-4cosxx鈮�0.511

Thus,

未=0.511-0未鈮�0.511

03

Step 3. Conclusion.

The largest value of未鈮�0.511.

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

In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

f(x)=(x-3),ifx<0-(x-3),ifx猢�0.

Calculate each of the limits:

limx鈫�01sec-1x.

For each of the following sign charts, sketch the graph of a function f that has the indicated signs, zeros, and discontinuities:

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

limx鈫�1x2-1x-1=2
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.