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The steps of the Newton-Raphson method to find the root of an equation f(x) = 0 are
1. Evaluate f¢(x) symbolically
2. Use an initial guess of the root, xi, to estimate the new value of the root xi+1 as
3. Find the absolute relative approximate error, 
as
4. Compare the absolute relative approximate error, with the pre-specified relative error tolerance, 
. If > , then go to step 2, else stop the algorithm. Also, check if the number of iterations has exceeded the maximum number of iterations.
Figure 1.Geometrical illustration of the Newton-Raphson method
Example 1:
You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for ABC commodes. The ball has a specific gravity of 0.6 and has a radius of 5.5 cm. You are asked to find the distance to which the ball will get submerged when floating in water.
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