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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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 t 0 e 5 t 1 t , t = ± 0.5 , ± 0.1 , ± 0.01 , ± 0.001 , ± 0.0001

To determine

To guess: The value of limt0e5t1t.

Explanation

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

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