to get the Maclaurin use the formula :
where is nth derivative...
so it goes
and so on .... and u have :
i think u can do that
Q: Find the Maclaurin polynomial of order 3 for the function f(x) = e^(-2x).
I know that the Maclaurin polynomial for e^x = 1 + x + x^2/2! + x^3/3! + ...
So my question is if I would have to plug in (-2x) in the Maclaurin polynomial of e^x so I get
e^(-2x) = 1 - 2x + 2x^2 - 4x^3/3 + ...
Is this right or wrong?
I know the formula I was just looking to see some work to see if I did the problem correctly. In another problem that I had in an exam consisted of the Maclaurin polynomial of 1/(1-x) = 1 + x + x^2 + X^3 + ...
and the professor wanted us to find the power series representation of 1/(1-x^3) and to figure that out you needed to put an x^3 wherever there was an x in the original given equation.
So I thought since I know the Maclaurin polynomial of e^x I thought that you were able to plug in (-2^x) wherever there was an x in that original polynomial.
just to note that when u mentioned that one that is from when we had have a lot of times to find or which are just a derivate of and actually using that Maclouren u can have a lot of another to do based on that one, you just have to tune it so it looks like that one
there is like 5 - 10 depending on school to school that u should know by heart and everything goes around them (at least here )
Edit:just remembered something to note