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# The Newton-Raphson Method

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The Newton-Raphson Method
1. Consider the function .

i) Show, graphically or otherwise, that the equation has a root in the interval (1,2). Show that .

ii) Use the secant method, with the function f(x) and starting values, 1 and 2, to find an estimate of correct to three decimal places.

2. Verify that has just one real zero and that it lies between 0 and 1 and give solution to five decimal places using the Newton-Raphson method.

3. Locate all the zeros of .

https://brainmass.com/math/recurrence-relation/newton-raphson-method-consider-function-380660

#### Solution Preview

See the attached files.

The Newton-Raphson Method

1. Consider the function .

i) Show, graphically or otherwise, that the equation has a root in the interval (1,2). Show that .

We have and Since is continuous on and it follows by the Intermediate Value Theorem that there exists a real number in the in the open interval such that Then and therefore

ii) Use the secant method, with the ...

#### Solution Summary

The Newton-Raphson Method is clearly exemplified in the solution. It verifies that a function has one real zero and that it lies between 0 and 1.

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