BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.2, Problem 17E
To determine

To guess: The limit of the function limx3x23xx29.

Expert Solution

Answer to Problem 17E

The limit of the function is guessed to 0.5.

Explanation of Solution

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.

xx23xx29f(x)=x23xx29
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, limx3+x23xx29=0.5.

Evaluate the function (correct to 6 decimal places) when x=2.9,2.95,2.99,2.999 and 2.9999 as shown in the below table.

xx23xx29f(x)=x23xx29
2.9−0.29−0.590.491525
2.95−0.1475−0.29750.495798
2.99−0.0299−0.05990.499165
2.999−0.003−0.0060.499917
2.9999−0.0003−0.00060.499992

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

That is, limx3x23xx29=0.5.

Since the right hand limit and the left hand limits are the same, limx3x23xx29 exists.

Therefore, the limit of the function is guessed to 0.5.

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