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Question Number 79359 by ahmadshahhimat775@gmail.com last updated on 24/Jan/20 Commented by mathmax by abdo last updated on 24/Jan/20 $${let}\:{A}_{{n}} =\frac{\left({n}!\right)^{\frac{\mathrm{1}}{{n}}} }{{n}}\:\:{we}\:{have}\:{n}!\:\sim{n}^{{n}} {e}^{−{n}} \sqrt{\mathrm{2}\pi{n}}\left(\:{stirling}\:{formulae}\right)\:\Rightarrow \\ $$$$\left({n}!\right)^{\frac{\mathrm{1}}{{n}}}…
Question Number 144816 by liberty last updated on 29/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{6x}^{\mathrm{2}} }−\left(\mathrm{1}+\mathrm{7x}\right)}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}−\mathrm{3}\right)}\:=? \\ $$ Answered by imjagoll last updated on 29/Jun/21 $$\:=−\frac{\mathrm{1}}{\mathrm{3}}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{6x}^{\mathrm{2}} \right)−\left(\mathrm{1}+\mathrm{14x}+\mathrm{49x}^{\mathrm{2}}…
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Question Number 79236 by jagoll last updated on 23/Jan/20 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\mathrm{x}\left\{\mathrm{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \right\}=? \\ $$ Commented by mathmax by abdo last updated on 23/Jan/20 $${let}\:{A}\left({x}\right)={x}\left\{{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \right\}\:\:{we}\:{have}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}}…
Question Number 144744 by mondlihk last updated on 28/Jun/21 Answered by Olaf_Thorendsen last updated on 28/Jun/21 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\frac{{x}−\mathrm{1}}{{y}−\mathrm{1}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}\:=\:\mathrm{1} \\ $$ Terms of Service Privacy…
Question Number 144622 by phally last updated on 27/Jun/21 Answered by alcohol last updated on 27/Jun/21 $${e}^{\frac{\mathrm{1}}{\mathrm{2}{a}}} \\ $$ Answered by mathmax by abdo last…
Question Number 144564 by imjagoll last updated on 26/Jun/21 Commented by justtry last updated on 26/Jun/21 $$\mathrm{0}?? \\ $$ Answered by liberty last updated on…
Question Number 144556 by imjagoll last updated on 26/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{x}^{\mathrm{2}} }\right)\:=? \\ $$ Answered by liberty last updated on 26/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{x}^{\mathrm{2}} }\right)=? \\…
Question Number 144558 by imjagoll last updated on 26/Jun/21 $$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(\frac{\mathrm{2x}−\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}}}{\mathrm{x}−\mathrm{1}}\right)=? \\ $$ Answered by liberty last updated on 26/Jun/21 $$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(\frac{\mathrm{2x}−\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3x}}}{\mathrm{x}−\mathrm{1}}\right)=? \\…