(You may want to maximize your window to see the solution more clearly.)
We want to determine the limit:
We observe that this expression appears to approach ∞0, which is indeterminate. However, applying the natural log gives,
That is, ln y = 1, giving us eln y = e1 or y = e (recall that eln y = y because ln x and ex are inverse functions).
Thus, y = e for all values of x > 1 (because the expression is not defined at x = 1).
Thus, l'Hospital's Rule is not needed here. Again, a graph helps:
Graph of 
for x > 2
(Note that the graph is constant for all x;
that is, it is the horizontal line y = e.)
