Change of Sign Failure When can the sign change method fail? There are certain circumstances where a change of sign fails to appropriately reflect the number or existence of roots If the interval i...
Change of Sign What does a change of sign mean? A sign change between f(a) to f(b) means there must be a root between a and b When an equation cannot be solved using the usual analytical methods, w...
Modelling with Parametric Equations What can be modelled with parametric equations? A common use for parametric equations is motion in two dimensions x = f(t) – horizontal position, dependent on ti...
Parametric Integration How does integration work with parametric equations? Integration is used to find the area under a curve where the curve has been defined by parametric equations x = f(t) y = ...
Parametric Differentiation How do I find dy/dx from parametric equations? Ensure you are familiar with Parametric Equations – Basics first This method uses the chain rule and the reciprocal propert...
Parametric Equations - Sketching Graphs How do I sketch a graph from parametric equations? Plotting a graph is covered in Parametric Equations - Basics Still find the key features of a graph … … th...
Parametric Equations - Eliminating the Parameter What does eliminating the parameter mean? In parametric equations, x = f(t) and y = g(t) There is still a connection directly linking x and y This w...
Parametric Equations - Basics What are parametric equations? Graphs are usually described by a Cartesian equation The equation involves x and y only Equations like this can sometimes be rearranged ...
Solving & Interpreting Differential Equations How do I solve a differential equation? Solving differential equations uses integration! The precise integration method will depend on the type of ...
