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 19E
To determine

To guess: The value of limt0e5t1t.

Expert Solution

Answer to Problem 19E

The limit of the function is guessed to 5.

Explanation of Solution

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.

te5te5t1f(t)=e5t1t
−0.50.082084999−0.917921.835830
−0.10.60653066−0.393473.934693
−0.010.951229425−0.048774.877057
−0.0010.995012479−0.004994.987520
−0.00010.999500125−0.00054.998750

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

That is, limt0e5t1t=5.

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

te5te5t1f(t)=e5t1t
0.512.1824939611.1824922.364987
0.11.6487212710.6487216.487212
0.011.0512710960.0512715.127109
0.0011.0050125210.0050135.012520
0.00011.0005001250.00055.001250

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

That is, limt0+e5t1t=5.

Since the right hand limit and the left hand limits are the same, limt0e5t1t exists.

Therefore, the limit of the function is guessed to 5.

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