8 The plot shows the function f(x) = 1 cos(x) x 2 , evaluated in MATLAB using the command (1 - cos(x)) / x^2. We plot the function between x = 109 and x = 106 , with a logarithmic scale for the x-axis. 107 109 108 107 106 0 0.5 1 x f(x) (a) (b) (c) (d) We notice large errors: the correct value of f(x) in this interval is very close to 1/2, because cos x 1x 2/2 for small x. We also note that the computed function is not continuous. (a) At what value of x does the first discontinuity (from point (a) to (b)) occur? Why is the computed value zero to the left of point (a)? (b) At what point does the second discontinuity occur (from point (c) to (d))? (c) What are the computed values at points (c) and (d)? (d) Give a more stable method for computing f(x) for small x. Be as precise as possible in your answers for parts (a), (b), and (c). However, you can use the approximation cos x 1 x 2/2