AGLIPAY, MARIA THERESE R. BSEE III-B Problem: Determine the first positive root (lowest positive root) of the equation 𝑦 = 𝑥 2 |sin 𝑥| − 4 (x is in radian) by the graphical and bisection methods. Use a stopping criterion below ∊𝑠 = 0.5% for the bisection method. Answer: f(x)= x2*(abs(sin(x)))-4 x 0.5 1 1.5 2 2.5 3 3.5 f(x) -3.880144 -3.158529 -1.755636 -0.362810 -0.259549 -2.729920 0.297095 In iteration 5, the percent absolute relative approximate error is 0.44843, which is less than ∊𝑠 = 0.5%. Therefore, the root is equal to 3.48438. AGLIPAY, MARIA THERESE R. BSEE III-B Iteration Xl Xr Xu f(Xl) f(Xr) f(Xl)*f(Xr) f(Xl)* f(Xr) Remarks (subinterval) 1 3 3.25 3.500 -2.729919927 -2.857188892 7.799896891 2 3.25 3.375 3.500 -2.857188892 -1.365418918 3.901259765 <0 2nd 3 3.375 3.4375 3.500 -1.365418918 -0.554242809 0.756773616 <0 2nd 4 3.4375 3.46875 3.500 -0.554242809 -0.13341449 0.073944022 <0 2nd 5 3.46875 3.484375 3.500 -0.13341449 0.080653783 -0.010760383 >0 1st Iteration Xl Xr Xu f(Xl)*f(Xr) f(Xl)* f(Xr) Remarks |∊𝒂 |, % (subinterval) 1 2 3 4 5 3 3.25 3.375 3.4375 3.46875 3.25 3.375 3.4375 3.46875 3.48438 3.500 3.500 3.500 3.500 3.500 f(Xl) f(Xr) -2.72992 -2.85719 7.799897 -2.85719 -1.36542 3.90126 -1.36542 -0.55424 0.756774 -0.55424 -0.13341 0.073944 -0.13341 0.080654 -0.01076 <0 <0 <0 >0 2nd 2nd 2nd 1st |∊𝒂 |, % 3.703703 704 1.818181 818 0.900900 901 0.448430 493 3.703704 1.818182 0.900901 0.44843