what does it mean to say taylor expansion of ex centered at 0? does it mean that the sum of the expansion will give me the value that the function ex will take when x = 0 ? so its e0 = 1? also, how do we know what value to center on? because as i encounter taylor series in my undergrad years, it seems that the professors all just say "taylor expanding this particular function, we have.. blah blah blah.." they don't seem to say centered about what? is it always assume to be centered upon 0? thanks!