   Chapter 2.2, Problem 45E

Chapter
Section
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 fEXAMPLE 9 FIGURE 15 (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.

 x x3−1 f(x)=1x3−1 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 1.5 2.375 0.421053 1.1 0.331 3.021148 1.01 0.030301 33.00221 1.001 0.003003 333.0002 1.0001 0

(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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