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Math
CalculusSingle Variable Calculus: Early Transcendentals8th Edition

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Chapter 2.2, Problem 19E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
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Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
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Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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 x → 3 x 2 − 3 x x 2 − 0 ,

x= 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999

To determine

To guess: The limit of the function limx→3x2−3xx2−9.

Explanation

Given:

The values of x are 3.1,3.05,3.01,3.001,3.0001,2.9,2.95,2.99,2.999 and 2.9999.

Calculation:

Since x approaches 3, the values 3.1,3.05,3.01,3.001, and 3.0001 are to the right of 3 and the values 2.9,2.95,2.99,2.999 and 2.9999 are to the left of 3.

Evaluate the function (correct to 6 decimal places) when x=3.1,3.05,3.01,3.001, and 3.0001 as shown in the below table.

xx2−3xx2−9f(x)=x2−3xx2−9
3.10.310.610.508197
3.050.15250.30250.504132
3.010.03010.06010.500832
3.0010.0030010.0060010.500083
3.00010.00030.00060.500008

Here, the value of f(x) gets closer to the value 0.5 as x approaches to 3 from the right side.

That is, limx→3+x2−3xx2−9=0

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