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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: a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x). b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)? c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as: a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x). b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)? c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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:

a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x).

b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)?

c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

We can express p and q as: p(x) Anx¹ + an_1x¹-1 + + 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. =
Transcribed Image Text:We can express p and q as: p(x) Anx¹ + an_1x¹-1 + + 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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