state the power series of an appropriate familiar function and use it to calculate the power series of the given function. give answer in sigma notation. All power series have center at 0.

Question

f(x)=(e^(-x)^2) -1+(x^2)

and

g(x)=x cos (x/square root 3)

Answer 1

f(x)=(e^(-x)^2) -1+(x^2)

= 1 - x^2 + x^4/2! - x^6/3! + ... -1 + x^2

= x^4/2! - x^6/3! + x^8/4! - ...