/*! 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. 18 Show that the limit as x鈫�2聽of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 18 (page 98)

Show that the limit as x鈫�2off(x)=x-1.1is not equal to 1, by finding an 蔚>0for which there is no corresponding 未>0satisfying the formal definition of limit.

Short Answer

Expert verified

The 未<0, the expression is false.

Step by step solution

01

Step 1. Given information.

The given function islimx鈫�2x-1.1鈮�1.

02

Step 2. Calculation.

From the given expression, we have, c=2,L=1.

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�2-未,2鈭�2,2+未thenx-1.1鈭�1-蔚,1+蔚.

So the largest value of 未is:

未=12-1.1-2未=1-1.1-2未=1-3.1未=-2.1

Since未<0, the expression is false.

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

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(x2-6x+5)=-4

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�0-f(x)=-1,limx鈫�0+f(x)=1,f(0)=0.

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

limx鈫�-6x+2=-4.

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

See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.