   Chapter 2.3, Problem 25E ### 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

# Evaluate the limit, if it exists. lim t → 0 1 + t − 1 − t t

To determine

To evaluate: The limit of the function limt01+t1tt.

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).

Difference of square formula: (a2b2)=(a+b)(ab)

Fact 1:

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

Evaluation:

Let f(t)=1+t1tt (1)

Note 1:

The direct substitution method is not applicable for the function f(t) since the function f(0) is in indeterminate form when t=0. That is,

f(0)=1+0100=110=110=00

Note 2:

The Quotient rule is not applicable for the function f(t) as the limit of the denominator is zero.

limt0(t)=0 (by limit law 8)

Note 3:

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

Calculation:

By note 3, take the limit h approaches zero but t0.

Simplify f(t) by using elementary algebra.

f(t)=1+t1tt

Take the conjugate of the numerator and multiply and divide by f(t)

### 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

#### In Problem 8-10, solve the inequality and graph the solution

Mathematical Applications for the Management, Life, and Social Sciences

#### f(x) = (x2 3)2 has points of inflection at x = _____. a) 0,3,3 b) 1, 1 c) 0, 1, 1 d) 3,3

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

#### Subtract 7516278 .

Mathematics For Machine Technology

#### Define content analysis and archival research.

Research Methods for the Behavioral Sciences (MindTap Course List) 