(a) Evaluate h(x) = (tan x – x)/x3 for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005.
(b) Guess the value of lim x→0 tan x – x / x3.
(c) Evaluate h(x) for successively smaller values of until you finally reach values for h(x). Are you still confident that your guess in part (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method for evaluating the limit will be explained.)
(d) Graph the function h in the viewing rectangle [– 1, 1] by [0, 1]. Then zoom in toward the point where the graph crosses the y-axis to estimate the limit of h(x) as x approaches 0. Continue to zoom in until you observe distortions in the graph of h. Compare with the results of part (c).