   Chapter 2, Problem 20RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the limit. lim x → 1 ( 1 x − 1 + 1 x 2 − 3 x + 2 )

To determine

To find: The limit of the function limx1(1x1+1x23x+2).

Explanation

Direct substitution property:

If f is a polynomial or a rational function and a is in the domain of f, then limxaf(x)=f(a).

Fact 1:

If f(x)=g(x) when xa, then limxaf(x)=limxag(x), provided the limit exist.

Evaluation:

Let f(x)=1x1+1x23x+2 (1)

Note 1:

The direct substitution method is not applicable for the function f(x) as the function f(1) is in an indeterminate form when x=1. That is,

f(1)=111+1123(1)+2=10+10=20

Note 2:

The limit may be infinite or it may be some finite value when both the numerator and the denominator approach 0.”

Calculation:

By note 2, consider the limit x approaches 1 but x1.

Simplify f(x) by using elementary algebra.

f(x)=1x1+1x23x+2 (2)

Factorise the denominator of f(x),

x23x+2=x22xx+2=x(x2)(x2)=(x1)(x2)

Substitute (x1)(x2) for x23x+2 in equation (2),

f(x)=1(x1)+1(x1)(x2)

Multiply and divide x2(0) in the first term of f(x)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Convert the expressions in Exercises 6584 to power form. x23

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 1124, find the indicated limits, if they exist. 21. limxx2x21

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Solve the equation in problem 1-6.; 5.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: n=21(lnn)n converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Solve: x(x+5)=1.

College Algebra (MindTap Course List) 