Question: (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 x0

(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).

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hx a tan x I x hx 055740773 037041992 033467209 005 033366700 001 033334667 0005 033333667 I 10 ... View full answer

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