I'm trying to develop an architecture hardware to make an implementation of an algorithm that can be descomposed in terms of sums, multiplications, subtractions and exponential functions. I'm trying to model $\exp(-x)$ through Taylor series. The domain of my function is bounded between $0$ and $1500$, but I want to use a particular Taylor approximation whose domain is bounded between $0$ and $0.5$.
Is there any way to get an approximation using the my Taylor series whose domain is bounded between $0$ and $0.5$ to model the function whose domain is bounded between $0$ and $1500$?
The function I want to model for bounded domain is $\exp(-x)$.
Thank you for your help.
You can certainly find the Taylor series of exp(-x) around 0.25. Wolfram Alpha gives an answer. Then you can plug large numbers into it if you want. It just won't be at all accurate. But I don't think I am understanding what you mean by your boldface question.