For the function...
... is...
... so that the McLaurin expansion is...
... and the series converges for any real or even complex x...
Kind regards
Hi I need help with this problem...
Construct the first three nonzero terms and the general term of the Maclaurin series generated by the function and give the interval of convergence:
In a page of my textbook it gives the general Maclaurin series for just cos(x) but when I ask my teacher whether it's just simply plugging in the (x+2), she says it's not. The question also gives the hint that but I am not sure what you can do with this hint?
cos(2)cos(x) = cos(2)(1 - x^2/2+......
sin(2)sin(x) = sin(2)(x +........
this should help now add them
or you could generate from scratch:
f(0) = cos(2)
f ' (0) = -sin(2)
f " (0) = -cos(2)
f(x) -> cos(2) -sin(2)x -cos(2)x^2/2
For the general term see attachment--for each k there are 2 terms