Newton-Raphson The Newton-Raphson method The Newton-Raphson method finds?roots?of equations in the form?f(x)?=?0 It can be used to find?approximate solutions?when an equation cannot be solved using...
x = g(x) Iteration What does ?mean?? When an equation cannot be solved using the usual?analytical methods, we can still find?approximate solutions?to a certain degree of accuracy Iteration?is one w...
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 proper...
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 … … t...
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 ...
