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?

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.



Then it starts over.

Yes, the 2x will make a difference:

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??