3 Question 3 The value of can be computed via const double pi = 4.0*atan2(1.0,1.0); The Bessel function Jo() can be computed by evaluating the following integral: In this question we approximate Jo(x) and compute the following sum and its derivative N-I S(z) = (3.2a) N-1 str) =-=-- (3.2b) sin(r sin . Set N 20 in this question We shall employ the Newton-Raphson algorithm to compute a root of S(z) = 0. Take the first 4 and last 4 digits of your student id. Define and as follows: (3.3) first 4 digits of your student id last 4 digits of your student id = For example if your student id is 23054617, then =0.2305 , 'b = 0 (3.4) Fill in the iterates in the tables below. Iterate until the value of z (solution for the root) converges to 3 decimal places. You can state the values of S(zi) to two significant figures, in each row I. Use ro= 1.0+Po for the initial iterate. converged to 3 d.p 2. Use r0-4.2+ for the initial iterate. 0120 = 4.2 + con to 3 d.p The function Jo(z) has an infinite number of roots. These are appronmations for the two smallest positive roots. 3 Question 3 The value of can be computed via const double pi = 4.0*atan2(1.0,1.0); The Bessel function Jo() can be computed by evaluating the following integral: In this question we approximate Jo(x) and compute the following sum and its derivative N-I S(z) = (3.2a) N-1 str) =-=-- (3.2b) sin(r sin . Set N 20 in this question We shall employ the Newton-Raphson algorithm to compute a root of S(z) = 0. Take the first 4 and last 4 digits of your student id. Define and as follows: (3.3) first 4 digits of your student id last 4 digits of your student id = For example if your student id is 23054617, then =0.2305 , 'b = 0 (3.4) Fill in the iterates in the tables below. Iterate until the value of z (solution for the root) converges to 3 decimal places. You can state the values of S(zi) to two significant figures, in each row I. Use ro= 1.0+Po for the initial iterate. converged to 3 d.p 2. Use r0-4.2+ for the initial iterate. 0120 = 4.2 + con to 3 d.p The function Jo(z) has an infinite number of roots. These are appronmations for the two smallest positive roots