taylor-series-use-cases.txt

Taylor Series are studied because polynomial functions are easy and if one could find a way to represent 
complicated functions as series (infinite polynomials) then one can easily study the properties of difficult functions.

Evaluating definite Integrals: Some functions have no antiderivative which can be expressed in 
terms of familiar functions. This makes evaluating definite integrals of these functions difficult 
because the Fundamental Theorem of Calculus cannot be used. If we have a polynomial representation 
of a function, we can oftentimes use that to evaluate a definite integral.

Understanding asymptotic behaviour: Sometimes, a Taylor series can tell us useful information about 
how a function behaves in an important part of its domain.

Understanding the growth of functions
Solving differential equations