# calculus

posted by .

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.

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

and

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

• calculus (#1` of 2) -

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! - ...

## Similar Questions

1. ### calculus - power series ASAP please :)

using power series, integrate & evaluate to 4 dec. places integral from 0 to 1: sin x^2 dx i'm REALLY stuck on this. and i need help asap.. what is the inverse of "sin x^2" so that i could have it in a fraction that will fit the power …
2. ### Calculus

Obtain the MacLaurin series for 1/(2-x) by making an appropriate substitution into the MacLaurin series for 1/(1-x). ------------ The MacLaurin series for 1/(1-x) = Σ x^k I substitue (x-1) in for x, because 1/(2-x) = 1/(1-(x-1)) …
3. ### Calculus

This is going to be pretty hard to show as text since it would be easier for me to post a picture of the question. The question has f(x) = x/4^2 - (2x^3)/4^4 + (3x^5)/4^6 + ... . I am trying to find out the value of f(2). There is …
4. ### Calculus II

(a) Use differentiation to find power series representation for f(x)=1/(1+x)^2 What is the radius of convergence?
5. ### Calculus

a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of …
6. ### Calculus

Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps?
7. ### Calculus

Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps?
8. ### Calculus 2

The following function has a series of the form the sum from n=0 to infinity of c(subn)x^n. Calculate the coefficients c(subn) and express the power series in summation notation. f(x)=(pi*x)/(pi*x+1) Thank you so much for your help!!!!
9. ### Integral Calculus

We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer …