Question

Why would you use a Taylor series instead of a Maclaurin series? A Maclaurin series seems a lot simpler since it is centered about 0, why would you ever want to work a problem not centered at 0 that would require the extra Taylor series complexity?

Answer 1

taylor series is centered about x=a .... so when a=0 then it is centered about x=0 which is known as maclaurin series (as aspecial case of taylor series)
we can not centre every series about 0 so taylor is used and it is standard form

Answer 2

Why can't you center every series about 0? Can you please give an example so that I will understand?

Taylor/Maclaurin series are polynomial representations of other functions, right? So, are you saying that you can't center every series at 0 because the series might represent a function that is undefined at 0?

Answer 3

e^(-1/x^2) if x not equal to 0
0 if x=0
it is not equal to its mac.. series
i m jst saying that it is not necessary that we have to calculate every series around 0 ... it can be asked to calculate about x=10 ,x=35,...etc so it is hard to calculate by mac..series

Answer 4

@JohnT got it buddy????

Answer 5

power series have an interval of convergence associated with them, if the value you are trying to determine is outside of a "zero centered" interval, then you need to shift your interval to be "centered" around a new value.