Wednesday, October 17, 2018

calculus - Evaluation of $ lim_{xrightarrow infty}frac{ln (x)}{x}$ using Squeeze theorem

Evaluation of $\displaystyle \lim_{x\rightarrow \infty}\frac{\ln (x)}{x}$ using sandwich Theorem (Squeeze theorem).



$\bf{My\ Try:}$ Let $\ln (x) = y\Rightarrow x=e^y$ and when $x\rightarrow \infty, y=\ln(x)\rightarrow \infty$




$\displaystyle \lim_{y\rightarrow \infty}\frac{y}{e^y}$, Now $\displaystyle e^y = 1+\frac{y}{1!}+\frac{y^2}{2!}+\frac{y^3}{3!}+..........+\infty$



Now I did not understand how I calculate The Given limit using Squeeze theorem



Help required



Thanks

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