Thursday, February 22, 2018

limits without lhopital - $lim_{ x to0^- }frac{2^{frac{1}{x}}+2^{frac{-1}{x}}}{3^{frac{1}{x}}+3^{frac{-1}{x}}}=?$

fine the limits-without-lhopital rule



$$\lim_{ x \to0^- }\frac{2^{\frac{1}{x}}+2^{\frac{-1}{x}}}{3^{\frac{1}{x}}+3^{\frac{-1}{x}}}=?$$



My Try :




$h= \frac{1}{x} :h\to - \infty$



so :



$$\lim_{ h\to - \infty }\frac{2^{h}+2^{-h}}{3^{h}+3^{-h}}=?\\\lim_{ h\to - \infty}\frac{(2^{-h})2^{2h}+1}{(3^{-h})3^{2h}+1}=?\\\lim_{ h\to - \infty }\frac{(2^{-h})2^{2h}+1}{(3^{-h})3^{2h}+1}=?$$



now :?

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