Question: Numerical Method. Please solve it with proper steps. 4. Consider the function f(x)=exex and the nodes are at 2,0, and 2 . Now answer the

Numerical Method. Please solve it with proper steps.

Numerical Method. Please solve it with proper steps. 4. Consider the function

4. Consider the function f(x)=exex and the nodes are at 2,0, and 2 . Now answer the following questions using 3 significant figures: (a) (4 marks) Evaluate the Newton coefficients ak=f[x0,,xk] using Newton's divided-difference method for the given function and nodes. (b) (3 marks) Compute the Newton interpolation polynomial for the given function, and express the result in the natural basis. Also use this polynomial to find an approximate value of f(6). (c) (3 marks) Evaluate the relative error in percentage form at x=1.5

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