You may have observed that the Lagrange interpolating p(x) always goes to ±∞ when x → ±∞. This may be explained by the following facts: ⚫ The Lagrange interpolating polynomial p(x) has degree N - 1 if it interpolates N points: ⚫ Given any polynomial q(x) = x + aм-1xΜ−¹ + ... + a₁ x² + do then lim x-100x q(x) = aм- Question 2 a. Prove the above limit equation. You may assume that the limit of a sum is the sum of the limits (when they exist), and that limx→∞ x = 0 if m<0. (This is a Calc 1 exercise. If you don't remember how to prove it, find a Calc 1 book. )
You may have observed that the Lagrange interpolating p(x) always goes to ±∞ when x → ±∞. This may be explained by the following facts: ⚫ The Lagrange interpolating polynomial p(x) has degree N - 1 if it interpolates N points: ⚫ Given any polynomial q(x) = x + aм-1xΜ−¹ + ... + a₁ x² + do then lim x-100x q(x) = aм- Question 2 a. Prove the above limit equation. You may assume that the limit of a sum is the sum of the limits (when they exist), and that limx→∞ x = 0 if m<0. (This is a Calc 1 exercise. If you don't remember how to prove it, find a Calc 1 book. )
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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