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calculate-lim-x-1-1-x-1-x-1-1-x-x-4-x-1-2-ln16-3-




Question Number 166922 by qaz last updated on 02/Mar/22
calculate  :   lim_(x→1) (((1+x)^(1/x) (1+(1/x))^x −4)/((x−1)^2 ))=ln16−3
$$\mathrm{calculate}\:\::\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} −\mathrm{4}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{ln16}−\mathrm{3} \\ $$

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