Find a power series for the function centered at 0.

Question

Find a power series for the function  centered at 0.

Quizplus · Accepted Answer

The power series centered at 0 for the function f(x) = e^x is given by ∑(n=0 to ∞) x^n/n!, which can be written as 1 + x/1! + x^2/2! + x^3/3! + ...
To get the power series for the function 11eaa595_645b_0c21_a696_cff23eb0ea6b_TB4584_11_TB4584_11, we just need to replace x with (x-11) in the power series for e^x:
∑(n=0 to ∞) [(x-11)^n/n!] = 1 + (x-11)/1! + (x-11)^2/2! + (x-11)^3/3! + ...
So the answer is C.

Find a Power Series for the Function Centered at 0