Exercise 1 - General understanding (3 marks) a) You are implementing on a comput

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Exercise 1 - General understanding (3 marks) a) You are implementing on a computer a numerical algorithm to solve an equation like f(x)-0. In order to check your algorithm you decide to test it with the function f(x)-x' (where you know that the exact solution is x = 0) Is this a good choice? Justify your answer b) Consider following functions. For each of them mention if it is possible to apply a bracketing method to locate their roots (if you cannot apply it give the reason) fi (x)-10-exp(x) f (x)=5+x-3 4 (x) = sin(x) (x)=(5x + 4)' c) During your work you have to solve a numerical problem which is the solution of a non

Explanation / Answer

(a)

No it is not a good choice because of the following reasons -

1. x^3 has only 1 roots i.e. 0, the algorithm can not be checked whether it can find multiple roots.

2. x =0 is a very simple root and can be most of the time the starting point from user, so the algorithm may not even be tested in full length. No iteration will be required in this case.

3. f(x) = x^3 has only one term and no constant term so you can never be sure about the efficiency of the algorithm.

please upvote the answer.

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