# OSA: Numerical Mathematics

## Question 1

Use three steps of Newton's method to compute approximate values of a root of the polynomial $$x^3-3x^2-x+3$$, starting with $$x_0 = 4$$. Give three digits after the decimal point.

$$x_1$$
$$x_2$$
$$x_3$$
Use Simpson's Rule (Newton-Cotes formula of degree two) to approximate the value of $\int_{-\sqrt{\ln 2}}^{\sqrt{\ln 2}} e^{-x^2}\,\mathrm{d}x.$ Give three digits after the decimal point.