   Chapter 3.4, Problem 69E

Chapter
Section
Textbook Problem

# (a) How large do we have to take x so that 1 / x 2 < 0.0001 ?(b) Taking r = 2 in Theorem 4, we have the statement lim x →   ∞ 1 x 2 = 0 Prove this directly using Definition 5.

To determine

a)

To find:

The value of x so that 1x2<0.0001

Explanation

1) Concept:

i) Let f be a function defined on an interval a, then limxfx=L means that for every ε>0 there is a corresponding number N such that if x>N then fx-L<ε

ii) If r>0 is a rational number then limx1xr=0

2) Calculation:

a) To find the value of x such that

1x2<0

To determine

b)

To prove:

limx1x2=0  by using definition 5

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