We will study the following function: f(x) = 1 - cos x x XXXXXXXXXXa) Start by plotting the function, using a grid of the form x = 0.1i for i = 1, 2,..., 100. This should give you some idea of the values you should expect for f(x) at small x. (b) Verify your previous hunch by taking the limit x ? 0 and using L'Hopital's rule. ? (c) Now, see what value you find for f(x) when x = 1.2 XXXXXXXXXXDoes this make sense, even qualitatively? (d) Use a trigonometric identity that enables you to avoid the cancellation. Evaluate the new function at x = 1.210-8 and compare with your analytical answer for x ? 0.

We will study the following function: f(x) = 1 - cos x x2 (2.96) (a) Start by plotting the function, using a grid of the form x = 0.1xi for i = 1, 2,.., 100. This should give you some idea of the values you should expect for f(x) at small x. (b) Verify your previous hunch by taking the limit x ? 0 and using L'Hopital's rule. * (c) Now, see what value you find for f(x) when x = 1.2 x 10-8 . Does this make sense, even qualitatively? (d) Use a trigonometric identity that enables you to avoid the cancellation. Evaluate the new function at x = 1.2x10-8 and compare with your analytical answer for x ? 0