# Exponential Limits

#### idontknow

(1) Evaluate $$\displaystyle L=\lim_{t\rightarrow 2 } \dfrac{2^t -t-2 }{t^2 -t -2 }$$.

(2) Evaluate $$\displaystyle L=\lim_{x\rightarrow \sqrt{3} } \dfrac{x^\sqrt{27} -\sqrt{27}^ x }{x-\sqrt{3}}$$.

#### RDKGames

Just apply L'Hopitals rule on both of them. Note that $$\displaystyle \displaystyle \dfrac{\mathrm{d}}{\mathrm{d}x}a^x = a^x \ln(a)$$