Hello, just thought i'd quickly say, I'm new here =].
I'm doing some problems on Taylors Series, like this one:
Find the Taylor polynomial of order 2 at x = a generated by the
function f(x) = sin(sin x) at a = 0:
I did this, coming to the correct answer by finding the 2 derivatives etc. The solutions however gave me this, which was a lot difference from my working:
sin(sin x) = sin x + O(sin^3 x) = x + O(x^3);
Hence P2(x) = x:
I was hoping somebody could perhaps explain the O symbol to me? and how sin(sin x) = sin c+ O(sin^3 x) etc.
Verify that (sin x)/x = 1 - (x^2)/6 + o(x^3)