Let f be a function that has derivatives of all orders on the interval (5, 7). Use the values in the table below and the formula for Taylor polynomials to give the 4" degree Taylor polynomial for f centered at c = 6: f(6) f' (6) f" (6) f" (6) f ( 4 ) ( 6 ) -3 4 8 9 -3 O 3 + x + 4x'+ 4x - 3 8 2 O -3+4(x - 6) +8(x - 6)' +9(x -6)3 -3(x -6)4 O -3x4+9x + 8x2 + 4x - 3 O -3+4(x - 6) +4(x -6)'+ -(x -6)3 - 3 = (2 - 6)4 O -3+4(x +6) +4(x +6)'+ = (x+6)3 - 8 (2 + 6 ) 4 O -3+4(x +6) +8(x +6)'+9(x +6)3 - 3(x+6)4 None of the above.Question number 5. Find the Taylor polynomial P (a ) centered at a = 0 for the function f(x) = e-9: O (-1)kak *=0 k! O E (-1)k+1gkk k! O (-1)*gkek k! n gk k O k! O k!Let P be the nth Taylor Polynomial of the function f( ) centered at a = 0. Assume that f is a function such that |f(")(@) | 1 for all n and a (the sine and cosine functions have this property.) Estimate the error if Pr is used to approximate f 8 ! O 8! O 7! O 6! O 7