Find a power series representation for the function. (give your power series representation centered at x = 0.) f(x) = x2/(x4 + 16)

Given the function:  

A geometric series is of the form of :

Now, rewrite the given function in the form of so that we can express the representation as a geometric series.

Now, divide numerator and denominator by we get;

=

Therefore, we now depend on the geometric series which is;

let then,

to get the power series let

so,

Multiply both side by we get;

or

or

Using

we have,

therefore, the power series representation centered at x =0 for the given function is:

1/2*qr*rs

step-by-step explanation:

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.