1 5. (Recursively Defined Sequences). (i) (a) Use a scientific calculator to find the terms 11, 12,..., I 10 of the sequence (In) recursively defined by ro = 3.8 and 38 2+1 = 2 + All terms ok must be rounded to seven decimal places after the period (as in 13.1415927), and presented in a table of the form 5), (n>0). IR 0 1 2 21 22 (b) In fact, it can be shown that the sequence (In) converges to the square root 38 of 38, and so find the relative error RE( 38 110) in approximation of 38 by 110- present your answer in (b), please type RE(38 110) ... below the table you will create in (a). (ii) (a) Use a scientific calculator to find the terms P1, P2, P3, ..., p7 of the sequence (Pn) recursively defined by po = 0.322 and Pn - cos(Pn) Pn+1 = Pn - (n > 0) 1 + sin(n) (make sure that your calculator is in radian mode when performing calculations of the terms pr.) The terms pk must be rounded to seven decimal places after the period and presented in a table similar to that one in (i). (b) In fact, the sequence (Pn) is the sequence gener ated by Newton's method with the initial approximation po = 0.322 for finding approximations of the root of the equation 1 - cos(x) = 0, and it converges to n. So use the Wolfram Alpha (Wa) website at https://volframalpha.com to find the 12-digit approximation of by entering the query ev alf( solve x-cos (x ) =0, 12) into the correspon ding webform (consult the Solution part of the output page). Find then the relative error REp7) and fix it below the table you will create in (a). To repeat, there must be two separate tables with answers to part (a) in (i) and (ii), respectively, and each table is to be followed by the corresponding relative error, as shown above