Use l'Hopital's Rule.
This is a limit → ∞.
Compare the powers on the top and bottom only.
Do not neglect their coefficients.
So this limit must be approaching +∞ or −∞.
This is Hana's Definition of the Derivative.
The limit is equal to f '(2) when f(x) = ex.
This is a limit → ∞. Be careful. Which is more powerful: an exponential function or a polynomial function?