the nth derivative is going to be valued at zero and that's what makes the Maclaurin series fairly straightforward if I want to approximate e^x using a maclaurin series so e^x and I'll put a little approximately over here and we'll get closer and closer to the real e^x and as we keep adding more and more terms especially if we add an infinite number of terms it would look like this: f(0) and we do it in what colors did I use for cosine and sine? pink and green