Hi I have some questions. If you're doing a MacLaurin expansion on a function say sinx or whatever, if you take an infinite number of terms in your series will it be 100% accurate? So will the MacLaurin series then be perfectly equal to the thing you're expanding? Also I don't really understand why, in a Taylor series, if you expand a function at x=5 (say) that it's more accurate for x near 5. Why is it different to an expansion of x=0? I can vaguely see that your chosen point of expansion, the value is perfect and it gets worse as you go away from it but is that good enough? I don't really understand what the remainder term does, can someone just explain it? Thanks. I promise I have looked on the net but I couldnt' find anything.