?Let P and Q be polynomials. Find if the degree of P is (a) less than the degree of Q

Chapter 2, Problem 55

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QUESTION:

Let P and Q be polynomials. Find

\(\lim _{x \rightarrow \infty} \frac{P(x)}{Q(x)}\)

if the degree of P is

(a) less than the degree of Q and

(b) greater than the degree of Q.

Questions & Answers

QUESTION:

Let P and Q be polynomials. Find

\(\lim _{x \rightarrow \infty} \frac{P(x)}{Q(x)}\)

if the degree of P is

(a) less than the degree of Q and

(b) greater than the degree of Q.

ANSWER:

Step 1 of 3

Given: Let  and  be polynomials. If the degree of  is (a) less than the degree of  and

(b) greater than the degree of then find .

.

Assume  and  be the given polynomials.

Then according to the given condition,

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