The radius of convergence simply means that the series does converges (no matter how slowly) inside that radius and does not converge outside it.
I don't see how it could be. A calculator does NOT use Taylor's series to calculate trig or exponential functions. See Internal Programming ofthe 9100A CalculatorThis question is related too to asking how does a graphic calculator calculate what sin(0.5) or cos(0.75) values are. Could anyone explain? I'd like something more visual or not too deep on maths, if possible.
Every power series is of the form . It is "centered around" .Also, what does it mean to say that the series is centered around x=0, or x=5?