13.You will get enough exercise on this topic in the Project.
5.1 X1. [8 pts] Using the methods we developed while studying Ch 0, compute a round-off error bound for the one-sided difference quotient (f(x+h)-f(x))/h. (Absolute error, not relative.) Using the truncation error formula given in class and the textbook, find the optimal value of h. 5.1 X2. [6 pts] Find a linear combination of f(x), f(x+h), f(x+2h) that is an approximation to f'(x) whose error is O(h2). 5.1 X4. [5 pts] Show by hand all the steps of the use of our simple differentiation arithmetic to evaluate the derivative of (x-3)2/(3x-7) at x=5. 5.2 Ex 1 [5 pts] (Composite Trapezoid Rule) May use Octave or Matlab if you wish. 5.2 Ex 3 [5 pts] (Composite Simpson's Rule) May use Octave or Matlab if you wish. 5.2 Ex X [6 pts] How many function evaluations would you need in order to be sure of getting full double precision accuracy in the evaluation of integral of the natural log from 1 to 2 using the composite Simpson's rule? 5.2 Ex 7 [6 pts] (Polynomial degree of several rules) (It suffices to see which monomials on [-1,1] the rule gets right. I.e. apply it to the functions 1, x, x2, x3, ... .)