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Numerical Methods

Newton Raphson Method

         

Let \( f(x) = x^3 − 72x − 220.\) Given that \(f(x)=0\) has a root near \( x = 12, \) compute \( x_1 \) by using Newton-Raphson method starting with \(x_0=12.\)

By using the Newton-Raphson method, find the positive root of the following quadratic equation correct to \( 5 \) significant figures: \[ x^2 + 9x – 5 = 0. \]

Start with \( x_0 = 2.2. \)

Use the Newton-Raphson method, correct to \( 5 \) significant figures, to get the root near \( x = 2\) of the equation \( f(x) = x^3 - 3x - 8.\)

The equation \( f(x) = 4e^x - 12 \) has a root near \( x = 1. \) Use the Newton-Raphson method to calculate the root correct to \( 5 \) significant figures.

Let \( f(x) = 4 x^2 − 8. \) Which of the following is the correct representation of \( x_{n+1} \) that Newton-Raphson method leads to?

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