Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as: d/Under what condition does r(x) have no horizontal asymptote? e/ Under what conditions does r(x) have a horizontal asymptote at y = 0? f/ Under what condition does r(x) have a horizontal asymptote at y = c, where c ̸= 0? What is the value of c in this case?
Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as: d/Under what condition does r(x) have no horizontal asymptote? e/ Under what conditions does r(x) have a horizontal asymptote at y = 0? f/ Under what condition does r(x) have a horizontal asymptote at y = c, where c ̸= 0? What is the value of c in this case?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as:
d/Under what condition does r(x) have no horizontal asymptote?
e/ Under what conditions does r(x) have a horizontal asymptote at y = 0?
f/ Under what condition does r(x) have a horizontal asymptote at y = c, where c ̸= 0? What is the value of c in this case?
Transcribed Image Text:We can express p and q as:
p(x)
Anx¹ + an−1xn−1 +
+ ao
and
q(x) = bmxm + bm-1xm. +
+ bo
where (i). all aj, b¡ are constants, (ii). m, n ≥ 0 are constant integers, and (iii). an, bm ‡ 0.
=
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