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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

(a) Use numerical and graphical evidence to guess the value of the limit

lim x 1 x 3 1 x 1

(b) How close to I does x have to be to ensure that the function in pan (a) is within a distance 0.5 of its limit?

(a)

To determine

To guess: The value of limx1x31x1 with the numerical and the graphing evidence.

Explanation

Calculation:

As x approaches 1, evaluate the function f(x)=x31x1 for the numbers 0.99,0.999,0.9999,1.01,1.001 and 1.0001.

Evaluate the function (correct to 6 decimal places) for the values of x and get the following table of values.

xx31x1f(x)=x31x1
0.99−0.0297−0.0050125635.925312
0.999−0.003−0.0005001255.992503
0.9999−0.0003−0.00005000135.99925
1.010.0303010.0049875626.075313
1.0010.0030030.0004998756.007503
1.00010.00030.00004999886.00075

From table, it is observed that the value of f(x)=x31x1 gets closer to 6 as x approaches to 1 from the either side

(b)

To determine

How close to 1 does 5.5x6.5 in part (a).

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