👉 Learn how to evaluate a piecewise function. A piecewise function is a function which uses different rules for different intervals. When evaluating a piecewise function, pay attention to the ...

Of course this produces the same derivative values as the usual limit-based definitions of the derivative. What makes this possibly preferable to the usual formulas, though, is that it arises out of ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.