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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) Evaluate the function f(x) = x2 – (2x/1000) for x = 1, 0.8, 0.6, 0.4, 0.2, 0. 1, and 0.05, and guess the value of

lim x 0 ( x 2 2 x 1000 )

(b) Evaluate f(x) for x = 0.04, 0.02, 0.01, 0.005, 0.003, and 0.001. Guess again.

(a)

To determine

To guess: The value of limx0(x22x1000) by evaluating the function f(x)=x22x1000 for the numbers x=1,0.8,0.6,0.4,0.2,0.1, and 0.05.

Explanation

Evaluate the function (correct to 6 decimal places) for the given numbers and obtain the following table of values.

xx22x1000f(x)=x22x1000
110.0020.998000
0.80.640.0017410.638259
0.60.360.0015160.358484
0.40.160.001320.158680
0.20.040.0011490.038851
0.10.010.0010720.008928
0.050

(b)

To determine

To guess: The value of limx0(x22x1000) by evaluating the function f(x)=x22x1000 for the numbers x=0.04,0.02,0.02,0.005,0.003 and 0.001.

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