# To guess: The value of lim h → 0 ( 2 + h ) 5 − 32 h . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### 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 limh→0(2+h)5−32h.

Expert Solution

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)5−32 f(h)=(2+h)5−32h −0.5 7.59375 −24.4063 48.812500 −0.1 24.76099 −7.23901 72.390100 −0.01 31.20796 −0.79204 79.203990 −0.001 31.92008 −0.07992 79.920040 −0.0001 31.992 −0.008 79.992000

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)5−32 f(h)=(2+h)5−32h 0.5 97.65625 65.65625 131.312500 0.1 40.84101 8.84101 88.410100 0.01 32.80804 0.80804 80.804010 0.001 32.08008 0.08008 80.080040 0.0001 32.008 0.008001 80.008000

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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