Ok, so I am suppose to use a power series function that we were given in our book to help me find a Maclaurin series for the following functions
f(x)=xcos(2x) and
f(x)=cos2x
Now, I assume I am going to use the following power series (which was given to me)..
cosx≈1−2!x2+4!x4−6!x6+...+(2n)!(−1)nx2n
Now I have a good idea of how I am going to do cos^2(x) .. using trig identities..
cos2x=21+cos(2x)
But.. Im not really sure how to go about doing the xcos(2x) .. would that be basically ...
xcosx≈x−2!x3+4!x5−6!x7+...
Then multiplied by a 2^n ?
Just sort of checking my work here , help would be much appreciated!
f(x)=xcos(2x) and
f(x)=cos2x
Now, I assume I am going to use the following power series (which was given to me)..
cosx≈1−2!x2+4!x4−6!x6+...+(2n)!(−1)nx2n
Now I have a good idea of how I am going to do cos^2(x) .. using trig identities..
cos2x=21+cos(2x)
But.. Im not really sure how to go about doing the xcos(2x) .. would that be basically ...
xcosx≈x−2!x3+4!x5−6!x7+...
Then multiplied by a 2^n ?
Just sort of checking my work here , help would be much appreciated!