[10 points] In the bulletin board of the course, a fellow student derived the following error propagation formula for the division of two numbers, x and y, with floating-point representations fl(x) = x(1 +81) and fl(y) = y(1 +82), respec- tively, x(1 +81) x 1 +81 +d3 fl(x) = fl(y) (1 +83) (1) y(1 +82) y where we assume 18 ;| s mach, for i = 1,2,3. Bring (1) in the form 1 +82 (1 +0.) y and derive a bound for 8.1, of the form 18-1 s CE mach with c a small constant number that you derive. Show your mathematical manipulation. 1 Hint: Use appropriate Taylor series of the function [10 points] In the bulletin board of the course, a fellow student derived the following error propagation formula for the division of two numbers, x and y, with floating-point representations fl(x) = x(1 +81) and fl(y) = y(1 +82), respec- tively, x(1 +81) x 1 +81 +d3 fl(x) = fl(y) (1 +83) (1) y(1 +82) y where we assume 18 ;| s mach, for i = 1,2,3. Bring (1) in the form 1 +82 (1 +0.) y and derive a bound for 8.1, of the form 18-1 s CE mach with c a small constant number that you derive. Show your mathematical manipulation. 1 Hint: Use appropriate Taylor series of the function