Taylor Series at x = 0 is the Maclaurin Series.
It says that a function f(x) can be approximated by an infinite series:
f(x) = f(0) + f'(0) * x + f''(0) * x^2/2! + f'''(0) * x^3/3! + ...
If f(x) = e^x then all the derivatives are also e^x and at x = 0 are all 1.
So f(x) = 1 + x + x^2/2! + x^3/3! + ... = sum[n=0 to inf][x^n/n!] = e^x.
f(-x) = 1 - x + x^2/2! - x^3/3! + ... = sum[n=0 to inf][(-1)^n * x^n/n!] = e^(-x).
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