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# (a) Evaluate $h(x) = (\tan x - x)/x^3$ for $x$ = 1, 0.5, 0.1, 0.05, 0.01, and 0.005.(b) Guess the value of $\displaystyle \lim_{x \to 0}\frac{\tan x - x}{x^3}$.(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 part (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method of 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 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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Limits

Derivatives

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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#### Topics

Limits

Derivatives

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp