Taylor Series, centered at 0, for f(x) = 1 / (4 + x^2)

[KaylaW1708]

The question is what is the Taylor Series centered at 0 for the function f(x) = 1/(4+x^2). I know that i have to take the derivative and plug in zero for each one. I'm not sure how many derivatives i have to take but for f'(x) i have -2x(4+x^2)^-2. the second derivative is (8x^2(4+x^2)^-3)-(2(4+x^2)^-2) There are other questions that go along with this problem but i have to know this part first.

 

[Deleted member 4993]

Re: Taylor Series

The question is what is the Taylor Series centered at 0 for the function f(x) = 1/(4+x^2). I know that i have to take the derivative and plug in zero for each one. I'm not sure how many derivatives i have to take

That depends on how much accuracy you are looking for. The residual of the Taylor series will give you the upper bound on the error for truncation.

For practical problems, we do not generally go beyond four terms.

but for f'(x) i have -2x(4+x^2)^-2. the second derivative is (8x^2(4+x^2)^-3)-(2(4+x^2)^-2) There are other questions that go along with this problem but i have to know this part first.