   Chapter 3.4, Problem 43E

Chapter
Section
Textbook Problem

# Let P and Q be polynomials. Find lim x → ∞ P ( x ) Q ( x ) if the degree of P is (a) less than the degree of Q and (b) greater than the degree of Q.

To determine

(a)

To find:

limxP(x)Q(x) if the degree of P is less than the degree of Q

Explanation

1) Concept:

Use limit property

2) Calculation:

limxP(x)Q(x)

By using limit property, divide numerator and denominator by the highest power of x in denominator

If degree of P is less than the degree of Q then after applying limit, numerator becomes 0

Therefore,

To determine

(b)

To find:

limxP(x)Q(x) if the degree of P is greater than the degree of Q

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