   Chapter 3.4, Problem 67E

Chapter
Section
Textbook Problem

# For the limit lim x →   ∞ 1 − 3 x x 2 + 1 = − 3 illustrate Definition 6 by finding values of N that correspond to ε = 0.1  and ε = 0.05 .

To determine

To find:

The values of N to illustrate Definition 6.

Explanation

1) Concept:

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

2) Given:

limx-1-3xx2+1=3

3) Calculation:

To find the values of N such that for x<N, 1-3xx2+1-3<ε i.e 3-ε<1-3xx2+1<3+ε

Therefore when ε=0.1 the value of the function lies between 3-0

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