Evaluate
![\[ \lim_{t \to 0} \tan t. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-a6ba53e7aa754fc1bdb2ae049ccca9bc_l3.png "Rendered by QuickLaTeX.com")
From Example 3 (p. 134 in Apostol) we know that the sine and cosine function are continuous. Since 
and 
is not zero at 
, we have that 
is continuous. Thus, we can take the limit by evaluating at ,
![\[ \lim_{t \to 0} \tan t = \lim_{t \to 0} \frac{\sin t}{\cos t} = 0. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-67413f4debb5d2979bfec0c87a7c9bb2_l3.png "Rendered by QuickLaTeX.com")
Evaluate
From Example 3 (p. 134 in Apostol) we know that the sine and cosine function are continuous. Since and is not zero at , we have that is continuous. Thus, we can take the limit by evaluating at ,