How do calculators quickly produce the values of transcendental functions? For instance, how does a calculator calculate tan 1.5? The calculator does not use series or polynomial approximation, but rather the CORDIC method. The following papers present the elementary ideas of the CORDIC method and show how it can be extended to nearly all function evaluations.
Given a third or fourth degree polynomial, what is the formula for explicitly finding its roots?
Continuity, differentiability and the Implicit Function Theorem for functions of two variables.