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Evaluate the limit


    \[ \lim_{t \to 0} \tan t. \]

From Example 3 (p. 134 in Apostol) we know that the sine and cosine function are continuous. Since \tan t = \frac{\sin t}{\cos t} and \cos t is not zero at t = 0, we have that \tan t is continuous. Thus, we can take the limit by evaluating at t = 0,

    \[ \lim_{t \to 0} \tan t = \lim_{t \to 0} \frac{\sin t}{\cos t} = 0. \]

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