1. ## Taylors Series Confusion

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.

Another is:

Verify that (sin x)/x = 1 - (x^2)/6 + o(x^3)

Thanks =]

2. Originally Posted by Redtwit
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.
Use the indentity...

(1)

... and then find the McLaurin expansion of each exponential in (1) proceeding as in...

http://www.mathhelpforum.com/math-he...nz-178887.html

Kind regards

$\chi$ $\sigma$

3. Originally Posted by Redtwit
Hello, just thought i'd quickly say, I'm new here =].

Verify that (sin x)/x = 1 - (x^2)/6 + o(x^3)
Starting from the well known...

(1)

... deviding both terms by x You obtain...

(2)

Kind regards

$\chi$ $\sigma$