   Chapter 2.2, Problem 21E ### 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

# Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places). lim t → 0 e 5 t − 1 t ,   t = ± 0.5 ,   ± 0.1 ,   ± 0.01 ,   ± 0.001 ,   ± 0.0001

To determine

To guess: The value of limt0e5t1t.

Explanation

Given:

The values of t are 0.5,0.1,0.01,0.001,0.0001,0.5,0.1,0.01,0.001 and 0.0001.

Calculation:

Since t approaches 0, the values 0.5,0.1,0.01,0.001, and0.0001 are to the left of 0 and the values 0.1,0.01,0.001 and 0.0001 are to the right of 3.

Evaluate the function (correct to 6 decimal places) when t=0.5,0.1,0.01,0.001, and0.0001 as shown in the below table.

 t e5t e5t−1 f(t)=e5t−1t −0.5 0.082084999 −0.91792 1.835830 −0.1 0.60653066 −0.39347 3.934693 −0.01 0.951229425 −0.04877 4.877057 −0.001 0.995012479 −0.00499 4.987520 −0.0001 0.999500125 −0.0005 4.998750

Here, the value of f(t) gets closer to the value 5 as t approaches 0 from the left side

### 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 Exercises 7-12, refer to the following figure. 8. What are the coordinates of point B?

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

#### In Problems 51 and 52, rationalize the numerator of each fraction and simplify. 52.

Mathematical Applications for the Management, Life, and Social Sciences

#### Divide: 4x212x6

Elementary Technical Mathematics

#### For y = x sin x, y = _____. a) x cos x b) x cos x + 1 c) cos x d) x cos x + sin x

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