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 20E
To determine

To guess: The value of limh0(2+h)532h.

Expert Solution

Answer to Problem 20E

The value of limit is guessed to 80.

Explanation of Solution

Given:

The values of h are h=±0.5,±0.1,±0.01,±0.001, and ±0.0001.

Calculation:

Since h approaches 0, the values 0.5,0.1,0.01,0.001, and 0.0001 are to the left of 0 and the values 0.5,0.1,0.01,0.001, and 0.0001 are to the right of 0.

Evaluate the function (correct to 6 decimal places) when h=0.5,0.1,0.01,0.001, and 0.0001 as shown in the below table.

h(2+h)5(2+h)532f(h)=(2+h)532h
−0.57.59375−24.406348.812500
−0.124.76099−7.2390172.390100
−0.0131.20796−0.7920479.203990
−0.00131.92008−0.0799279.920040
−0.000131.992−0.00879.992000

Here, the value of f(h) approaches 80 as h closer to 0 from the left side.

That is, limh0(2+h)532h=80.

Evaluate the function (correct to 6 decimal places) when h=0.5,0.1,0.01,0.001, and 0.0001 as shown in the below table.

h(2+h)5(2+h)532f(h)=(2+h)532h
0.597.6562565.65625131.312500
0.140.841018.8410188.410100
0.0132.808040.8080480.804010
0.00132.080080.0800880.080040
0.000132.0080.00800180.008000

Here, the value of f(h) approaches 80 as h closer to 0 from the right side.

That is, limh0+(2+h)532h=80.

Since the right hand limit and the left hand limits are the same, the value of limh0(2+h)532h exists.

Therefore, the limit of the function is guessed to 80.

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