# Taylor series approximation problem

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Lingbai Ren on 15 Sep 2021
Commented: Lingbai Ren on 24 Sep 2021
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!

Matt J on 15 Sep 2021
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 on 24 Sep 2021
Sorry Matt for the late reply, I think what works, but I finally wrote a whole for loop to run that! Thanks for helping!

R2021a

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