   Chapter 3.4, Problem 25E

Chapter
Section
Textbook Problem

# 9-32 Find the limit or show that it does not exist. lim x →   ∞ x 4 − 3 x 2 + x x 3 − x + 2

To determine

To find:

lim ∞x4-3x2+xx3-x+2

Explanation

1) Concept:

To evaluate the limit at infinity of any rational function, first divide both the numerator and denominator by the highest power of x that occurs in the denominator.

2) Formula:

i) Quotient law:limp(x)q(x)= limx p(x)limx q(x)

ii) Sum law: lim[px+ qx]=limp(x)+ limq(x)

iii) Difference law:lim[px- qx]=limp(x)- limq(x)

iv) Constant multiple law: limc.p(x)=c.limp(x)

v) Constant law: lim ∞c =c

3) Given:

lim ∞x4-3x2+xx3-x+2

4) Calculation:

Here, highest power of denominator is 3 so divide by x3 to numerator and denominator

lim ∞x4-3x2+xx3-x+2=lim ∞x4x3-3x2x3+xx3x3x3

### 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

#### Proof Prove that lnxy=ylnx.

Calculus: Early Transcendental Functions

#### Define sampling with replacement and explain why is it used?

Statistics for The Behavioral Sciences (MindTap Course List)

#### limx2x2(x1)1x = _____. a) 4 b) 1 c) 0 d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 