Originally Posted by

**AfterShock** With linear approximations, there are also error bounds. For problems that you're unable to get an equality, an approximation is the next best thing. They can be especially useful (more so when you know HOW useful it is); I completely disagree with:

"If you are asking for mathematics, then the answer is no purpose at all."

Consider other approximations, such as Riemann sums or taylor polynomials. Do these serve no purpose at all, for an integral (for instance) that cannot be found exactly?