The function needs to be defined and infinitely differentiable at the point that it is centred.
Am I right in thinking that a Maclaurin or less specifically Taylor series is the infinite sum representation of a function?
So If I want to calculate e^5 exactly and I had infinite time and patience, that If I calculated out:
That I would arrive at the value for e^5?
If so, then I've seen it works with trig functions, log functions and x to the power of some changing variable. It also works for fractions of all of those... Are there any limitations? Or can ANY function be represented as a Maclaurin or Taylor series
You would have some basic knowledge about the family of functions you'll be dealing with. It's all to do with "experience".
When I say defined, I mean needs to be in the domain of your function.
E.g. you can't have a Taylor series for centred at , because is not defined.
You CAN however have it centred around , because IS defined.