ABSTRACT
This chapter defines the special number e and its consequences. It describes the exponential function and its inverse and the natural logarithm function. The theory of Riemann integration is utilized to define the special number e. The special number e is provided as the limit of a particular sequence of rational numbers. The chapter describes Bernoulli’s Identity and the exponential function. The question of continuity is a question of interchanging the order of limit operations. The chapter discusses the properties of the exponential function and looks at Taylor polynomials for some familiar functions. Continuity of the inverse function is described along with differentiability of the inverse function. The chapter reviews the properties of the natural logarithm, logarithm function plots, exponential function plots, and L'Hopital’s rules.
