   Chapter 3.R, Problem 8E

Chapter
Section
Textbook Problem

# 7-12 Find the limit. lim t →   ∞ t 3 − t + 2 ( 2 t − 1 ) ( t 2 + t + 1 )

To determine

To find:

The limit limtt3- t + 2(2t - 1)(t2 + t + 1)

Explanation

1) Concept:

To evaluate the limit at infinity of any rational function, divide the numerator and thedenominator by the highest power of 𝑡that 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) Theorem:

If r > 0 is a rational number then

limx 1xr=0

4) Given:

limtt3-t+2(2t-1)(t2+t+1)

5) Calculation:

limtt3-t+22t-1t2+t+1

=limtt3-t+22t3+t2+t-1

Divide the numerator and the denominator by the highest power of t that occurs in the denominator which is  t3

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