   Chapter 3.R, Problem 9E

Chapter
Section
Textbook Problem

# 7-12 Find the limit. lim x →   − ∞ 4 x 2 + 1 3 x − 1

To determine

To find:

The limit limx-4x2 + 13x - 1

Explanation

1) Concept:

To evaluate the limit at infinity of any rational function, divide the numerator and the 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: lim[px+qx]=limp(x)+limq(x)

iii) Quotient law: limpxqx =limp(x)limq(x)

iv) Constant law: lim ∞c =c

v) Root law: limxp(x)n=limxp(x)n

3) Theorem:

If r > 0 is a rational number such that xr is defined for all x, then limx -1xr=0

4) Given:

limx-4x2 + 13x - 1

5) Calculation:

Divide the numerator and denominator by the highest power of x that occurs in the denominator which is x2 since x can be written as x2

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