Exponential Limits

Dec 2015
973
128
Earth
(1) Evaluate \(\displaystyle L=\lim_{t\rightarrow 2 } \dfrac{2^t -t-2 }{t^2 -t -2 }\).

(2) Evaluate \(\displaystyle L=\lim_{x\rightarrow \sqrt{3} } \dfrac{x^\sqrt{27} -\sqrt{27}^ x }{x-\sqrt{3}}\).
 
Jun 2016
11
14
UK
Just apply L'Hopitals rule on both of them. Note that \(\displaystyle \displaystyle \dfrac{\mathrm{d}}{\mathrm{d}x}a^x = a^x \ln(a)\)