I'm studying power series / taylor series, but I'm having understanding how the different pieces relate. I have a few questions:
1) Both the power and Taylor series has a center, but what does c represent? (i.e. if at infinity, the polynomial approximation is very close to the original function, why not just set c=0, or remove the variable altogether)
2) How does c relate to interval of convergence if at all?
3) Why does adding n-th derivative makes the polynomial a more accurate representation of the original function? (i.e. why not subtract, or multiply?)