Evaluate following limits.

Solution

In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this,

Hence, the exponent goes to minus infinity in the limit and thus the exponential has to go to zero in the limit.  Hence, the answer is,

Let's work on some more complicated examples including exponentials.  In the following examples it won't be that the exponents are more complexes, but instead that there will be more than one exponential function to deal with.