Consider the function defined by

Determine whether the sequence converges or diverges, and if it converges find the limit.

We use the definition of the exponential and some tricks to get into a form we know how to deal with,

The final line follows since

since

Therefore,

Thus, converges to the limit 0.

Would it still be valid to express the question as

and just claim the limits of both the numerator and denominator approach 0?