/*! 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. 81 Use the Squeeze Theorem to find ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 81 (page 136)

Use the Squeeze Theorem to find the limits. Explain exactly how the Squeeze Theorem applies in each case.

limx鈫�0ex-1sin1x

Short Answer

Expert verified

The limit of the given equation is 0.

Step by step solution

01

Step 1. Given information.

Consider the given question,
limx鈫�0ex-1sin1x

02

Step 2. Apply squeeze theorem.

Range of sin1xor sinxis -1,1.

-1鈮�sin1x鈮�1

Multiply all the sides by ex-1,

-1ex-1鈮�sin1xex-1鈮�1ex-1-ex+1鈮�sin1xex-1鈮�ex-1

Applying limits on all the sides as x鈫�0,

limx鈫�0-ex+1鈮�limx鈫�0sin1xex-1鈮�limx鈫�0ex-1-e0+1鈮�limx鈫�0sin1xex-1鈮�limx鈫�0鈮�e0-1-1+1鈮�limx鈫�0sin1xex-1鈮�1-10鈮�limx鈫�0sin1xex-1鈮�0

Applying the Squeeze theorem,

=0

03

Step 3. Plot the graph.

Representing the graph, we get,

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�0+ln1+x

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)=x2,ifx<24,ifx=22x+1,ifx>2.

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�3(x+5)=8

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

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

limx鈫�23x2-12x+15=3.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.