Reasons for using Rolle's Theorem in calculus are discussed, with comparisons to the theorems of Lagrange and Cauchy. (MNS)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

An approach to polynomial approximations that leads the student to stumble on Taylor's theorem and its proof is presented, with a generalization. (MNS)

A proof for a limit is given, with a recommended presentation consisting of three lemmas followed by the theorem. (MNS)

Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

A calculus problem on finding the maximum volume of a box is discussed, with extensions to various types of boxes. (MNS)

A definition of convexity with six conditions is discussed and illustrated. (MNS)

Two traditional presentations introducing the calculus of exponential functions are first presented. Then the suggested direct presentation using calculators is described. (MNS)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)