ABSTRACT
This chapter helps the reader to evaluate simple limits using the laws of limits and decide, in simple cases, whether a function is continuous or not. It helps the reader to perform the processes of elementary differentiation, obtain higher-order derivatives of a product using Leibniz’s theorem, and apply differentiation to calculate rates of change. The chapter also demonstrates solving practical problems concerning cylinder pressure and the seepage of water into soil. It presents the rules which are often known as the laws of limits. If the right-hand side exists then the left-hand side exists and the two are equal; if the right-hand side does not exist, then the rule cannot be applied. It is not always possible to simplify an expression, but if it is a product or a quotient it may help to ‘take logarithms’ before differentiating. By this means we avoid the use of the product rule, but more importantly we avoid the very awkward quotient rule.
