Taylor Series Calculator

This calculator expands five functions whose derivatives are known exactly: e^x, sin x, cos x, ln(1+x) and the geometric series 1/(1-x). Choose one, give the centre and the highest power to keep, and it returns every term, the Taylor polynomial and the interval where the series converges. A second mode evaluates that polynomial at a point and sets it beside the real value, so the size of the error is visible rather than assumed. Nothing else is supported: there is no symbolic differentiation here, so a function outside those five cannot be expanded by this tool.