QUESTION 6 (a) The function et is to be approximated by a fifth-order polynomial over the interval [-1, +1]. Why is a Chebyshev series a better choice than a Taylor (or Maclauring) expansion? (b) Given the power series and the Chebyshev polynomials f(x)=1-x-2x³-4x² To (x) T₁ (x) T₂ (x) T3 (x) = 1 = X = 2x² - 1 = 4x³ - 3x T4(x) = 8x48x² +1, economize the power series f(x) twice. (c) Find the Padé approximation R3 (x), with numerator of degree 2 and denominator of degree 1, to the function f(x) = x² + x³.

QUESTION 6 (a) The function et is to be approximated by a fifth-order polynomial over the interval [-1, +1]. Why is a Chebyshev series a better choice than a Taylor (or Maclauring) expansion? (b) Given the power series and the Chebyshev polynomials f(x)=1-x-2x³-4x² To (x) T₁ (x) T₂ (x) T3 (x) = 1 = X = 2x² - 1 = 4x³ - 3x T4(x) = 8x48x² +1, economize the power series f(x) twice. (c) Find the Padé approximation R3 (x), with numerator of degree 2 and denominator of degree 1, to the function f(x) = x² + x³.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

See similar textbooks