The problem is ths one
The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x = 5 is given by f^(n)(5) = ((-1)^n(n!)0/(2^n(n+2), and f(5)=1/2.
Write the third-degree Taylor polynomial for f about x = 5.
Find the radius of convergence of the Taylor series for f about x = 5.
Show that the sixth-degree Taylor polynomial for f about x = 5 approximates f(6) with error less than 1/1000
So far i have for part a) f(5)+f'(5)(x-5)+(1/2!)f''(5)(x-5)^2+(1/3!)f'''(5)(x-5)^3
how do i find my f'(5), f''(5)......
Im not sure about the rest of the problem
The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x = 5 is given by f^(n)(5) = ((-1)^n(n!)0/(2^n(n+2), and f(5)=1/2.
Write the third-degree Taylor polynomial for f about x = 5.
Find the radius of convergence of the Taylor series for f about x = 5.
Show that the sixth-degree Taylor polynomial for f about x = 5 approximates f(6) with error less than 1/1000
So far i have for part a) f(5)+f'(5)(x-5)+(1/2!)f''(5)(x-5)^2+(1/3!)f'''(5)(x-5)^3
how do i find my f'(5), f''(5)......
Im not sure about the rest of the problem