User:Graemeb1967/Sandbox


 * $$\sin^2 \theta + \cos^2 \theta = 1.\!$$


 * $$1 + \tan^2 \theta = \sec^2 \theta\,$$

and


 * $$1 + \cot^2 \theta = \csc^2 \theta\,$$


 * $$\begin{matrix}

x_1 & = & x_0 - \dfrac{f(x_0)}{f'(x_0)} & = & 10 - \dfrac{10^2 - 612}{2 \cdot 10} & = & 35.6 \quad\quad\quad{} \\ x_2 & = & x_1 - \dfrac{f(x_1)}{f'(x_1)} & = & 35.6 - \dfrac{35.6^2 - 612}{2 \cdot 35.6} & = & \underline{2}6.3955056 \\ x_3 & = & \vdots & = & \vdots & = & \underline{24.7}906355 \\ x_4 & = & \vdots & = & \vdots & = & \underline{24.7386}883 \\ x_5 & = & \vdots & = & \vdots & = & \underline{24.7386338} \end{matrix} $$