Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues' formula and integration by parts to show that 1 L' f(x)P, (x)dx = (1) m² | (x² - f(x)Pn(x)dx (x²-1)" fm (x)dx. ... Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0 for ij, and if F= c1fi+C2f2+...+cmfm Show that Ck= (F, fk) ||fk||2

Question 2: Let f possess a continuous nth-order derivative on the interval [—1, 1]. Use Rodrigues' formula and integration by parts to show that 1 L' f(x)P, (x)dx = (1) m² | (x² - f(x)Pn(x)dx (x²-1)" fm (x)dx. ... Question 3: If the functions f₁, f2, fm (not necessarily polynomials) are orthogonal, that is, (fi, fj) = 0 for ij, and if F= c1fi+C2f2+...+cmfm Show that Ck= (F, fk) ||fk||2

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.5: Derivatives Of Logarithmic Functions

Problem 54E

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