po(x) =TagP2(x) ==Pn(x)=Choose one[1]X (k) 12(k + 1)!k=0รk=0=P4 (2) = {1}–k=0z2k(-1) 72k(2k)!m2k(−1)k²k(2k)!รX (1)k!k=02kzkP1(x) =pg(x) == Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and thenfind the nth Maclaurin polynomial for the function in sigma notation.COS(TX)Po(x) =P₂(x) =P4(x) =P₁(x) =-P3(x):-

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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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1.F.3 One of my favorite bases of P<4 is X = {1,x,2x² – 1,4x3 – 3r, 8x“ – 822 + 1}. Find the coordinates of 1, x, x², x³, and xª with respect to X. Aside: These polynomials are called Chebyshev polynomials (of the first kind). You may remember your trig identity cos(26) = 2 cos²(8) – 1. If x = cos(0) then cos(20) = 2x² – 1. Similarly, cos(30) = 4.x3 – 3x and cos(40) = 8x4 – 8x² +1. So, when you found the coordinates of x4 above, you secretly found a way to write cos (0) as a linear combination of {1, cos(0), cos(20), cos(30), cos(40)}.
Find the Maclaurin polynomials of orders n = 0, 1,2, 3, and 4 and then find the nth Maclaurin polynomial for the function in sigma notation. 19 cos(T2) Po(x) p1(x) =| Choose one P2(x) =|| (-19k)²,2* (k + 1)! P3(x) = k=0 [n] (-1)*1972 (2k)! k=0 p1(x) =|| 51 (-1)*197* k! k=0 = (x)"d (-1)*1972* (2k)! k=0 EW! EW! EWI EWI
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Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polynomial for the function in sigma notation. COS(TX)