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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.

questionanswerresultexplanation

\(x_1\)

\(x_2\)

\(x_3\)

Question 2

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.