Paul's Online Notes
Home / Calculus I / Limits / Limits At Infinity, Part II
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 2.8 : Limits at Infinity, Part II

11. Evaluate $$\displaystyle \mathop {\lim }\limits_{t \to \,\infty } {\tan ^{ - 1}}\left( {\frac{{4 + 7t}}{{2 - t}}} \right)$$.

Show Solution

First notice that,

$\mathop {\lim }\limits_{t \to \,\infty } \frac{{4 + 7t}}{{2 - t}} = - 7$

If you aren’t sure about this limit you should go back to the previous section and work some of the examples there to make sure that you can do these kinds of limits.

$\mathop {\lim }\limits_{t \to \,\infty } {\tan ^{ - 1}}\left( {\frac{{4 + 7t}}{{2 - t}}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{{{\tan }^{ - 1}}\left( { - 7} \right)}}$