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Newton raphson method for finding root

 Newton Raphson MethodThe Newton Raphson method is for solving equations of the form f(x) = 0. We make an initial guess for the root we are trying to find, and we call this initial guess x0.The sequence x0, x1, x2 ,x3, . . . generated in the manner described below should con-verge to th...

Find the square root of 612 with an error less than 10-4 by newton-rapson method.

Find the square root of 612 with an error less than 10-4 by newton-rapson method.

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We have to find x such that 

 x2=612

The derivative of 

f(x) = x2-612

is f’(x) = 2x

With an initial guess of x0=10, the sequence given by the method is 

X1= x0 -(f(x0) /f'(x0)) = 10-(102-612)/(2*10)= 35.6

x2 = x1 - (f(x1)/f'(x1)) = 26.3955056

Similarly,

x3 = 24.7906355

x4 = 24.7386883

x5 = 24.7386338

Where the correct digits are underlined.

f(24.7386338) = (24.7386338)2-612 = 0.0000022905 <10-4

The required square root is 24.7386338.

More questions on OOP Concept

Find the square root of 2 with an error less than 10-4 by bisection method.

The function involved is f(x) = x2-2. The following table steps through the iteration until the size of the interval, given in the last column is less than 0.01.

Hence, the answer is (1.41406+1.42187)/2= 1.417


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