Concept explainers
(a) Evaluate h(x) = (tan x – x)/x3 for x = 1, 0.5, 0.1 , 0.05, 0.0 1, and 0.005.
(b) Guess the value of
(c) Evaluate h(x) for successively smaller values of x until you finally reach a value of 0 for h(x). Are you still confident that your guess in pan (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method for evaluating this 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 they-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 pan (c).
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Chapter 2 Solutions
Calculus: Early Transcendentals
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- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning