Taylor series approximation problem

we are considering a Taylor series approximation of f(x) = e^(-x)

my questions is how to compute the Taylor Series approximation of f(x).

The requirements are: the code should take as input x_i, x_i+1, and the order, n.

The code should output the normalized true error e_T, at x_i+1

I'm totally lost where to start, hope to get some hints or help!

thanks!

Answer 1

[Matt J]

As an example,

syms x

T=taylor(exp(-x),x,7,'Order',4)

T = 

fn=matlabFunction(T)

fn = function_handle with value:
    @(x)exp(-7.0)-exp(-7.0).*(x-7.0)+(exp(-7.0).*(x-7.0).^2)./2.0-(exp(-7.0).*(x-7.0).^3)./6.0

fn(3)

ans = 0.0216

You can of course find more examples in the documentation for taylor() and matlabuUnction()

[Lingbai Ren]

Sorry Matt for the late reply, I think what works, but I finally wrote a whole for loop to run that! Thanks for helping!