   Chapter 4.5, Problem 68E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using the Definition of Limits at Infinity Consider lim x → − ∞ 3 x x 2 + 3 (a) Use the definition of limits at infinity to find the value of N that corresponds to ε = 0.5 .(b) Use the definition of limits at infinity to find the value of N that corresponds to ε = 0.1 .

(a)

To determine

To calculate: The value of N that corresponds to a value of 0.5 for ε as per the definition of infinite limits where limx3xx2+3

Explanation

Given:

The expression limx3xx2+3.

Formula Used:

The statement limxf(x)=a implies that for every ε>0 there would exist an N>0 such that the following conditions holds whenever x<N:

|f(x)a|<ε

Calculation:

Consider the provided expression:

limx3xx2+3

The limit can be found by dividing the numerator and denominator by x:

limx3xx2+3=limx31+3x2=31+limx3x2=31+0=−</

(b)

To determine

To calculate: The value of N that corresponds to a value of 0.1 for ε as per the definition of infinite limits where limx3xx2+3

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