   Chapter 3.4, Problem 10E

Chapter
Section
Textbook Problem

# 9-32 Find the limit or show that it does not exist. lim x → ∞ 1 − x 2 x 3 − x + 1

To determine

To find:

limx1-x2x3-x+1

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) Difference Law:limx px-qx=limx px-limx q(x)

ii) Sum Law: limx px+qx=limx px+limx q(x)

iii) Quotient Law:limx pxq(x)=limxp(x)limxq(x)

3) Given:

limx1-x2x3-x+1

4) Calculation:

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

limx1-x2x3-x+1=limx1-x2x3(x3-x+1)x3

=limx1x3-1x1-1x2+1x3

By using quotient law of limit,

limxș

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