Analogy to the purpose of Taylor series I want to know an analogy to the purpose of Taylor series. I did a google search for web and videos : all talks about what Taylor series and examples of it. But no analogies. I am not a math geek and this is my attempt to re-learn Calculus in a better way, to understand Physics and Linear Algebra. 
Having an analogy will indeed help to view its use in real life. Learning seems lacking, if  the concept can't be applied. Appreciate a more laymen term explanation at this challenging point (for me).
Have read this post as of now: What are the practical applications of Taylor series?. That post (the answers, comments) indeed increases the bar of my expectation for a satisfying answer to my question.

Taylor series can be taken as laying down an imitation of the function curve which is trying to be like it. The points that affect Taylor series are:- 


*

*The point where your focus is; (x = a)

*The number of terms you use for precision.


As you increase the terms; i.e. the more inner depth secrets of function's making(higher derivatives;) , the more closer you will go to the function's approximation.
Similarly; the focus point; is the point where you are starting to calculate the higher derivatives; and prediction. It can be taken as launching pad of Taylor series. The curve approximation is best in that point's surrounding.
We use Taylor series to express any function in the form of power series; so that further visualization; and calculations would become easy.
For example:- If i expand cosine function with the use of Taylor series; then it would become easy for a person to calculate its approximated value for a particular value of domain of that function.
