   Chapter 2.2, Problem 19E

Chapter
Section
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 x → 3 x 2 − 3 x x 2 − 0 , x= 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999

To determine

To guess: The limit of the function limx3x23xx29.

Explanation

Given:

The values of x are 3.1,3.05,3.01,3.001,3.0001,2.9,2.95,2.99,2.999 and 2.9999.

Calculation:

Since x approaches 3, the values 3.1,3.05,3.01,3.001, and 3.0001 are to the right of 3 and the values 2.9,2.95,2.99,2.999 and 2.9999 are to the left of 3.

Evaluate the function (correct to 6 decimal places) when x=3.1,3.05,3.01,3.001, and 3.0001 as shown in the below table.

 x x2−3x x2−9 f(x)=x2−3xx2−9 3.1 0.31 0.61 0.508197 3.05 0.1525 0.3025 0.504132 3.01 0.0301 0.0601 0.500832 3.001 0.003001 0.006001 0.500083 3.0001 0.0003 0.0006 0.500008

Here, the value of f(x) gets closer to the value 0.5 as x approaches to 3 from the right side.

That is, limx3+x23xx29=0

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