Consider the function f(x) = 1 − cos(x) x 2 . (a) evaluate limx→0 f(x) = l. (b) as x → 0, at what rate does f(x) → l? (c) compute f(x) as written on a computer for values of x = 10−1 , 10−2 , . . , 10−10. comment on your results. (d) suppose that we are able to represent floating point numbers with n decimal digits of accuracy. around what value of r will the evaluation of f(x) produce very large relative errors when |x| < r? (e) rearrange the expression for f(x) to a mathematically equivalent expression so that the this new function evaluates accurately for very small values of x. verify the success of your rearrangement computationally. a