For a quadratic equation of the form ax^2+bx+c=0, the discriminant function b^2-4ac is introduced, as a way of determining how many roots this equation has. This is then applied to problems of determining how many points of intersection the curves re...

Document(s)

Title

A demonstration of how to use the Newton-Raphson method: to find the positive solution of the equation x^2 = 2

Background to the method of differentiation by first principles

Example of using differention by first principles to evaluate the derivative of the function y = 1 divided by x

Example of using differentiation by first principles to evaluate the derivative of the function y = square root of x

Example of using differentiation by first principles to evaluate the derivative of a quadratic function.

Gives an example of calculating the first and second derivatives of a function where implicit differentiation is required

In this recording we look at a second example of how to write a composite hyperbolic function as an algebraic function of x.

An example of using integration to find the area of a region that is bounded by 2 curves

This recording demonstrates the general method for solving an equation of form sqrt(ax^2+bx+c) = cx+d and then illustrates this with an example, including checking solutions that were generated by squaring both sides to see which ones satisfy the ori...