Chapter 4.5, Problem 68E

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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 limxâ†’âˆ’âˆž3xx2+3.

Formula Used:

The statement limxâ†’âˆžf(x)=a implies that for every Îµ>0 there would exist an N>0 such that the following conditions holds whenever x<N:

|f(x)âˆ’a|<Îµ

Calculation:

Consider the provided expression:

limxâ†’âˆ’âˆž3xx2+3

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

limxâ†’âˆ’âˆž3xx2+3=limxâ†’âˆ’âˆžâˆ’31+3x2=âˆ’31+limxâ†’âˆ’âˆž3x2=âˆ’31+0=âˆ’</

(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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started