(a) Use numerical and graphical evidence to guess the value of the limit lim xl1 x3 2 1

Chapter 2, Problem 55

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QUESTION:

(a) Use numerical and graphical evidence to guess the value of the limit lim xl1 x3 2 1 sx 2 1 (b) How close to 1 does x have to be to ensure that the function in part (a) is within a distance 0.5 of its limit?

Questions & Answers

QUESTION:

(a) Use numerical and graphical evidence to guess the value of the limit lim xl1 x3 2 1 sx 2 1 (b) How close to 1 does x have to be to ensure that the function in part (a) is within a distance 0.5 of its limit?

ANSWER:

Problem 55

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

b) How close to 1 does x have to be in order to ensure that the function in part a is within 0.5 of its limit?

                                                              Step by Step Solution

Step 1 of 3

(a)

Make a table of values for the function  shown below:

x

f(x)

0.9

5.280931738

0.99

5.925312187

0.999

5.992503125

0.9999

5.999250031

1.0001

6.000750031

1.001

6.007503125

1.01

6.075312812

1.1

6.781557287

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