Consider the function f(x) 1 sin(x) (a) (3 points) Is f(x) well-conditioned or ill-conditioned for values...

 

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Consider the function f(x) 1 sin(x) (a) (3 points) Is f(x) well-conditioned or ill-conditioned for values of a close to ? Is f(x) well-conditioned or ill-conditioned for values of a close to 0.5? To answer this, do the following. Consider the condition number f'(x)/f(), and evaluate this for = 1.56 and = 0.51 in radians. (b) (3 points) What is the relative error in these two cases? Briefly explain how you interpret the condition number to arrive at your conclusions. Consider the function f(x) 1 sin(x) (a) (3 points) Is f(x) well-conditioned or ill-conditioned for values of a close to ? Is f(x) well-conditioned or ill-conditioned for values of a close to 0.5? To answer this, do the following. Consider the condition number f'(x)/f(), and evaluate this for = 1.56 and = 0.51 in radians. (b) (3 points) What is the relative error in these two cases? Briefly explain how you interpret the condition number to arrive at your conclusions.