The availability of sophisticated computer graphics provides an extremely powerful tool for investigating the geometrical aspects of many concepts and methods in mathematics. This is particularly applicable to calculus where much of the underlying material is geometric in nature. When teaching certain topics in calculus, most notably limits of indeterminate forms and logarithmic differentiation, we routinely deal with rather complex functions which are almost impossible to graph accurately by hand. In the present paper, a survey of some of the more interesting and surprising graphs which actually arise are displayed when the corresponding functions are viewed through the eye of the computer.