a) If q(n) = byn* + Bk-1n*-1+...+ b1n+ bo is a polynomial in the variable ne N with be # 0, show that there exists N EN such that n > N implies q(n) # 0. b) Show that aknk + ak-1nk-1+...+ a1n + ao lim n-00 bknk + bk-1nk-1+ + bịn + bo bk provided that b +0 and k is a positive integer.
a) If q(n) = byn* + Bk-1n*-1+...+ b1n+ bo is a polynomial in the variable ne N with be # 0, show that there exists N EN such that n > N implies q(n) # 0. b) Show that aknk + ak-1nk-1+...+ a1n + ao lim n-00 bknk + bk-1nk-1+ + bịn + bo bk provided that b +0 and k is a positive integer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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