Chapter 3.4, Problem 14E

Chapter
Section
Textbook Problem

# 9-32 Find the limit or show that it does not exist. lim x → ∞ t − t t 2 t 3 / 2 + 3 t − 5

To determine

To find:

limtt-tt2t32+3t-5

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: limpxqx=limp(x)limq(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: lim ∞c p(x)=clim ∞p(x)

v) Constant law: lim ∞c =c

3) Given:

limtt-t2t32+3t-5

4) Calculation:

Here, highest power of denominator is t32, divide numerator and denominator by t32

limtt-t2t32+3t-5=limtt-ttt322t32+3t-5t3

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