(You may want to maximize your window to see the solution more clearly.)
We want to determine the limit:
Can we apply l'Hospital's rule? First, let's look at the numerator. We know that
Therefore,
Next, we'll look at the denominator:
We can see that both the numerator and the denominator approach 0 as x approaches 0. Therefore, this rational expression gives us the indeterminate form 0/0, which allows us to use l'Hospital's Rule.
Applying l'Hospital's Rule, we get,
Applying l'Hospital's Rule again, we get
Using the limit theorems (the limit of a sum is the sum of the limits, and so forth), we can evaluate this limit,
Thus, the limit of the original expression is 2. A graph helps confirm this:
Graph of Curve 
near x = 0
