Casio ClassPad II Custom Commands

nmeth (Program)

Command last updated 7/2/2023.

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nmeth(f, xa, n)

Applies Newton’s method to approximate an x-intercept of f for n iterations. Prints the details of each iteration and returns the coordinates following the n-th iteration. Column i is the iteration number, x is \(x_i\), y is \(f(x_i)\), dy/dx is \(f'(x_i)\) and δx is \(x_{i+1} - x_i = - \dfrac{f(x_i)}{f'(x_i)}\).

Example

Find \(x_1\), \(x_2\) and \(x_3\) using Newton’s method with \(x_0 = 0\) to approximate an x-intercept of \(h(x) = 2^x - x^2\). (2023 Methods Exam 2 Section B Question 3f)

nmeth(2^x-x^2, 0, 3)

Contributed by Nhan