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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

Determine lim x 1 1 x 3 1 and lim x 1 + 1 x 3 1

(a) by evaluating f(x) = l/(x3 – 1) for values of x that approach 1 from the left and from the right,

(b) by reasoning as in Example 9, and

(c) from a graph of f

EXAMPLE 9

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FIGURE 15

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(a)

To determine

The value of limx11x31 and limx1+1x31 by evaluating the value of f(x)=1x31 for various x values that approach 1 from either side.

Explanation

As x approaches 1 from either side, evaluate the function f(x)=1x31 for the numbers 0.5,0.9,0.99,0.999,0.9999,1.5,1.1,1.01,1.001 and 1.0001.

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

xx31f(x)=1x31
0.5−0.875−1.14286
0.9−0.271−3.69004
0.99−0.0297−33.6689
0.999−0.003−333.667
0.9999−0.0003−3333.67
1.52.3750.421053
1.10.3313.021148
1.010.03030133.00221
1.0010.003003333.0002
1.00010

(b)

To determine

To explain: The reasons of the limits obtained in part (a).

(c)

To determine

To check: The answer obtained in part (a) by graphing the function f(x)=1x31 as x approaches 1 from either side.

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