Was there a specific problem that lead to need for developing Taylor Series?
I have (informally) heard that hundreds of years ago, people had difficulty calculating different things. This included:
- Logarithms
- Cube Roots
- Exponents where the power was a decimal number
- Complicated functions involving very large numbers
- etc.
I have also heard that these problems and difficulties lead to the development of different approximation methods to calculate these things, and the Taylor Series was one of these methods.
For example, suppose someone in the the 18th Century wanted to calculate the 4th Root of some large number (e.g. 999999) - using the Taylor Series, they could write this in general as "x^(1/7)", find the Taylor Expansion of this function around x = 999999, and finally calculate the approximation error bound relating to this calculation.
Is this correct?
Was the Taylor Series originally developed to approximate (and "bound") calculations that used to be difficult hundreds of years ago? Were there in fact some specific types of calculations that were giving people difficulties back then - Or was the Taylor Series purely developed as a theoretical exercise with no intended applications to real world problems?
Thanks!