⦁ Use the Bisection method to find for f (x) = on [0, 1].
⦁ Find an approximation to correct to within using the Bisection Algorithm. [Hint: Consider
⦁ Use a fixed-point iteration method to find an approximation to that is accurate to within . Compare your result and the number of iterations required with the answer obtained in Exercise 12 of Section 2.1. (exercise 12 is #2 above)
⦁ Let and . Use Newtons Method to find
⦁ Let and and , find
⦁ Use the Secant method.
⦁ Use the method of False Position
⦁ Which of a or b is closer to
⦁ Use Newton’s method to find solutions accurate to within to the following problem.
, for
⦁ For the given functions f(x), let Construct interpolation polynomials of degree at most one and at most two to approximate and find the absolute error.
⦁ Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials.
if
⦁ Determine the natural cubic spline S that interpolates the data f (0) = 0, f (1) = 1, and f (2) = 2.
⦁ Construct the natural cubic spline for the following data.
⦁ What is the Taylor series of the function
f(x) = x5 – 2×4 + 3×3 – 4×2 – 10x – 5
at the point c =17
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