2. ( Recursively Defined Seguences). (i) Study the following program for a scientific calcula tor for calcula ting the terms of the sequence (pn) recur sivdy 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(0.35x)0.17 (replace p0 and p1 in the program with the corresponding values given above, and replace f(I) and f(Y) with correct expressions representing the values of the function f given above; 5ay, f(I) should be replaced with Iain(0.35I)=0.17 Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms pn in a familiar programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calcula tor. (ii) Execute the program for a sci calcula tor to get the terme p2,p3,,p10 of the sequence ( pn ) (make 5 ure that your calcula tor is in it RADIAN mode). Present the results of your calcalations in a table of the form All terms pk must be rounded to eight decimal places a fter the period. (iii) It can be shown that in fact the sequence (pn), generated by the 50 -called Secant Method for root finding problem 5 , converges to ~ of by executing the command aolrex*ain(0.35x)=0.17in[0.1] at the website (click on the CMore digits button on the output page in order to get all ten digits of ~ if necessar y ). (iv) Find the rela tive err or RE(~p10) in the a pproximation of z by the term p10 you have found in (ii)