The behavior of certain functions in advanced calculus is discussed, with the mathematics explained. (MNS)

The behavior of some functions near the point of origin is discussed. Each function oscillates, and as x approaches 0, the oscillations become increasingly more rapid; their behavior near the origin improves with increasing values of n. Examples for a calculus class to consider are given. (MNS)

Described is an example of a piecewise defined function developed naturally as a consequence of the solution to the given problem statement, thereby allowing calculus students the uncommon opportunity to generate such an otherwise, seemingly contrived function. (JJK)

Because one of the difficulties with the standard presentation of the Fundamental Theorem of Calculus (FTC) is that essentially all functions used to illustrate this theorem are taken from earlier material, many students never fully appreciate the essential role played by continuity in statement and proof of FTC. Introduces the sim x function that…

Elementary error estimation in the approximation of functions by polynomials as a computational assignment, error-bounding functions and error bounds, and the choice of interpolation points are discussed. Precalculus and computer instruction are used on some of the calculations. (KR)

Presents several types of functions which fit a given set of data and create opportunities for classroom discussion comparing different kinds of functions and identifying some of the potential hazards associated with extrapolation from best-fit functions. (DDR)