I understand what a Taylor series is and how to find the Taylor series of a function. However I do not understand intuitively what it means to find a Taylor series for a specific function, centered at $x=a$ compared to $x=b.$ Can someone explain please?
[Math] What does it mean intuitively for a Taylor Series to be centered at a specific point
power seriestaylor expansion
Best Answer
Intuitively, it means that you are anchoring a polynomial at a particular point in such a way that the polynomial agrees with the given function in value, first derivative, second derivative, and so on. Essentially, you are making a polynomial which looks just like the given function at that point. [Then Taylor's theorem guarantees that if continued to an infinite number of terms, the series will be the same as the given function.]