Q2 R

2. (Recursively Defined Sequences). (i) St udy the following program for a scient ific calculator for calculating the terms of the sequence (pn) recursively defined by pn=pn1f(pn1)f(pn1)f(pn2)pn1pn2 for all n2, where p0=1andp1=0.8 and where the function f is given by f(x)=xsin(0.79x)0.40 (replace p0 and p1 in the program with the corresponding values given above, and replace f(X) and f(Y) with correct expressions representing the values of the function f given above; say, f(X) should be replaced with xsin(0.79x)0.40 Prior to st udying the above program, it is a good idea to start with creating your own program for calculating the ter ms pn in a familiar programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator. (ii) Execute the program for a sci calculator to get the ter ms p2,p3,,p10 of the sequence (pn ) (make sure that your calculator is in it RADIAN mode). Present the results of your calculations in a table of the form All terms pk must be rounded to eight decimal places after the period. (iii) It can be shown that in fact the sequence (pn) generated by the so-called Secant Method for root finding problems, convergesto the unique root of the function f in [0,1]. With this in mind, use the Wolframilpha (W, a) website to find the 10 -digit approximation ~ of bye executing the command solvexsin(0.79x)=0.40in[0.1] at the website (click oil the More digits button on the-outpit page in oill lo get all ten-digits of if necessary)