The use of the limit theory and how the function f^' (x)≈(f(x+h)-f(x))/h is manipulated to produce a secondary approximation equation is what is going to be investigated. Over the course of history, various techniques have been developed to help approximate complicated calculations. Through exploring the purpose of the limit theory and comparing it to that of the function that gives the gradient of a chord, conclusions can be made as to the effect the ‘h’ value has on the overall equation. From this, a secondary equation can be formed that allows the approximation of square roots and other functions to be evaluated. The purpose of this function within the mathematical world and its limitations are discussed.