Volume 2 : 3 ratio of the volumes of the sphere and cylinder is credited to Archimedes. The volume of a sphere is the integral of an infinite number of infinitesimally small circular disks of thickness "dx". The calculation for the volume of a sphere with center 0 and radius "r" is as follows. The surface area of the circular disk is formula_10. The radius of the circular disks, defined such that the x-axis cuts perpendicularly through them, is or where y or z can be taken to represent the radius of a disk at a particular x value. Using y
Radius of convergence If we expand the function around the point "x" = 0, we find out that the radius of convergence of this series is formula_50 meaning that this series converges for all complex numbers. However, in applications, one is often interested in the precision of a numerical answer. Both the number of terms and the value at which the series is to be evaluated affect the accuracy of the answer. For example, if we want to calculate accurate up to five decimal places, we only need the first two terms of the series. However, if we want the same precision for