How do you find the Taylor's formula for f(x)=e^x for x-2?

1 Answer
Sep 2, 2017

f(x) = e^2( 1 + (x-2) + (x-2)^2/2 + (x-2)^3/6 +...)

Explanation:

Did you mean find the Taylor series of f(x) about x = 2 ?

The Taylor expansion of a function about a point a is defined as

f(x) = f(a) + f'(a) (x-a) + (f''(a))/(2!) (x-a)^2 + (f'''(a))/(3!) (x-a)^3 + ... = sum_(n=0)^(oo) (f^((n))(a))/(n!) (x - a)^n

Taking a = 2 we have that

f(x) = e^2( 1 + (x-2) + (x-2)^2/2 + (x-2)^3/6 +...)

as the derivative of e^x is simply e^x.