idontknow Dec 2015 973 128 Earth Dec 19, 2019 #1 (1) Evaluate \(\displaystyle L=\lim_{t\rightarrow 2 } \dfrac{2^t -t-2 }{t^2 -t -2 }\). (2) Evaluate \(\displaystyle L=\lim_{x\rightarrow \sqrt{3} } \dfrac{x^\sqrt{27} -\sqrt{27}^ x }{x-\sqrt{3}}\).

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

R RDKGames Jun 2016 11 14 UK Jan 26, 2020 #2 Just apply L'Hopitals rule on both of them. Note that \(\displaystyle \displaystyle \dfrac{\mathrm{d}}{\mathrm{d}x}a^x = a^x \ln(a)\) Reactions: idontknow and topsquark

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