ACMMM107
use the increments formula: \(\delta y\cong\frac{dy}{dx}\times\delta x\) to estimate the change in the dependent variable \(y\) resulting from changes in the independent variable \(x\)
ACMMM107 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM124
examine the area problem, and use sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\) as area under the curve \(y=f(x)\)
ACMMM124 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM130
understand and use the theorem \(F'\left(x\right)=\frac d{dx}\left(\int_a^xf\left(t\right)dt\right)=f\left(x\right)\), and illustrate its proof geometrically
ACMMM130 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM149
determine and use the probabilities \(\mathrm P\left(\mathrm X=\mathrm r\right)=\begin{pmatrix}\mathrm n\\\mathrm r\end{pmatrix}\mathrm p^\mathrm r{(1-\mathrm p)}^{\mathrm n-\mathrm r}\) associated with the binomial distribution with parameters \(n\) …
ACMMM149 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum