= 1. (extra credit) Write down explicitly the 9th Taylor polynomial, expanded about x = 2, of f(x) = {$(+4 + 512 )dt. a

[answerhappygod]

1 Extra Credit Write Down Explicitly The 9th Taylor Polynomial Expanded About X 2 Of F X 4 512 Dt A 1 (55.57 KiB) Viewed 22 times

= 1. (extra credit) Write down explicitly the 9th Taylor polynomial, expanded about x = 2, of f(x) = {$(+4 + 512 )dt. a 2. (extra credit problem) The Vandermonde matrix gives rise to the array that determines a polynomial. Given the x-values, nodes, X0,X1, ... ,Xn-1, define xi xo 1 X0 ... . V.(x) 1 xn-1 X-1 1 x x2 Show that Vy(x) is a nth order polynomial with zeros the nodes: X0,X1, ... ,Xn-1.Obtain the formula V,(x) = 1,-1(xn-1)(x – xo)(x – x1)... (x – Xn-1). Hint: expand the last row of V,(x) by minors to show V,(x) is a polynomial of degree n and to find the coefficient of the term x"