Check out some similar questions!

dks2114 · Sep 27, 2007, 01:32 PM

Can some one explain to me where does the x come from in the Taylor series. In sin(x) = 1 + X/1! +...

Why is it x and if the function turned into sin (2x) does it affect that x?

galactus · Sep 27, 2007, 02:59 PM

If a function is infinitely differentiable, then that begins the Taylor series. Differentiable wrt to x.

Taylor series are an expansion and approximation to functions such as sin, e, etc.

$f(x)=sin(x), \;\ f'(x)=cos(x), \;\ f''(x)=-sin(x), \;\ f'''(x)=-cos(x), \;\ f^{4}(x)=sin(x)$

Then it starts over.

Yes, the 2x will make a difference:

$sin(2x)=2x-\frac{4x^{3}}{3}+\frac{4x^{5}}{15}-\frac{8x^{7}}{315}+\frac{4x^{9}}{2835}-........................................$

$sin(2x)=\sum_{k=0}^{\infty}(-1)^{k}\frac{(2x)^{2k+1}}{(2k+1)!}$

dks2114 · Sep 27, 2007, 08:28 PM

But does this method only work for certain functions (like trig and oiler's number) or can it work for let's say x^3??