Evaluate following limits.

Solution

Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the following diagram of inverse tangents. The left over two parts are more involved hence as along with the exponential & logarithm limits actually just refer back to the first two parts as we'll see.

As noted above all we actually have to do here is look at the graph of the inverse tangent.  Doing this illustrates us that we have the given value of the limit.