ABSTRACT
In the seventeenth century, Newton and Leibniz based much of the calculus they developed on the idea of taking limits. In spite of the success that calculus brought to the natural sciences, it also drew heavy criticism due to the use of infinitesimals (infinitely small numbers). This chapter reviews some of the rules for evaluating limits. Some of the easiest problems occur. The chapter continues our study by establishing various properties of limits. Once again, much of the material can be found in Cauchy’s Cours d’Analyse. It is always useful to be able to replace a complicated expression with a simpler one. Usually, this strategy requires that the expressions are equal. The chapter finds the exact limit of a convergent sequence. Unfortunately, this is often impossible, so we are forced to estimate the limit only approximately.
