   Chapter 2.2, Problem 49E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### 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.

 x x2 2x1000 f(x)=x2−2x1000 1 1 0.002 0.998000 0.8 0.64 0.001741 0.638259 0.6 0.36 0.001516 0.358484 0.4 0.16 0.00132 0.158680 0.2 0.04 0.001149 0.038851 0.1 0.01 0.001072 0.008928 0.05 0

(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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