What is the meaning of expansion of a function in calculus.What does it mean saying expansion of a function about a point.
For example i came across Taylor's expansion of a function f(x) about the point x=a which is given by
f(x)=f(a)+(x-a)f'(a)/1! + (x-a)^2*f"(a)/2!and so on ....
the formula looks simple and can be understood.But the honest question is ,what is expansion of a "function"?
[Difficulty]
the most provoking and confusing part is the word "expansion"
when it comes to expansion this is what one would think
i,e something like (x+y)^2(the whole square) ,(x+y+z)^3 and etc
how should i understand expansion in calculus and the one mentioned above ((x+y)^2(the whole square) ,(x+y+z)^3)
how is it different from the one mentioned above [i,e (x+y)^2(the whole square) ,(x+y+z)^3]
[Thoughts]
I am sorry , i understand expansion to be that of a binomial
expansion ,or in general a polynomial . i,e (x+y)^2=x^2+2xy+y^2.What is expansion of f(x) is still a question
Thank you
>Krish