Given the function squareroot 4x^2 - 0.04 + 0.24sin^-1(0.1/x) = 10.055752 Use th

Question

Given the function squareroot 4x^2 - 0.04 + 0.24sin^-1(0.1/x) = 10.055752 Use the Bisection method and the false-position methods to solve the equation f(x) = 0. (Assume epsilon_s = 0.001%) Use the Calculator to find the true value of the root. Use the value obtained in (b) to compute the true percentage error. Use the formula to calculate the number of iteration necessary to achieve the desired percentage approximation relative error. Compare the results obtained from both methods based on speed and accuracy.

Explanation / Answer

False position methode:

We have shown the iterations untill we get exact root.

Iteration 0 : a = 2 : b = 10 c = 2 f(x) -6.04875
Iteration 1 : a = 5.02543 : b = 10 c = 5.02543 f(x) -0.00209742
Iteration 2 : a = 5.02648 : b = 10 c = 5.02648 f(x) -2.89167e-07
Iteration 3 : a = 5.02648 : b = 10 c = 5.02648 f(x) -3.98579e-11
Iteration 4 : a = 5.02648 : b = 10 c = 5.02648 f(x) -7.10543e-15
The value of root is : 5.02648

Bisection methode:

So, from above data, we can say that False position methode is more accurate and fast as compared to bisection methode for the particular situation.

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