Question Number 129211 by bramlexs22 last updated on 13/Jan/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{cos}\:\left(\sqrt{\mathrm{x}}\:\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }\:=?\: \\ $$ Answered by liberty last updated on 13/Jan/21 $$\:\mathcal{L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{cos}\:\left(\sqrt{\mathrm{x}}\:\right)^{\frac{\mathrm{1}}{\mathrm{x}}} } \\…
Question Number 129199 by Adel last updated on 13/Jan/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\frac{\mathrm{x}^{\mathrm{x}+\mathrm{1}} }{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{x}} }−\frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{x}} }{\mathrm{x}^{\mathrm{x}−\mathrm{1}} }\right]=? \\ $$$$\mathrm{solve}\:\:\:\mathrm{tish}\:\:\mathrm{pleas} \\ $$ Answered by mr W last updated…
Question Number 63579 by Tawa1 last updated on 05/Jul/19 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{2}^{\mathrm{sec}\left(\mathrm{x}\right)} \:−\:\mathrm{2}^{\mathrm{cos}\left(\mathrm{x}\right)} }{\mathrm{x}^{\mathrm{2}} } \\ $$ Commented by Prithwish sen last updated on 05/Jul/19 $$\because\:\mathrm{form}\:\frac{\mathrm{0}}{\mathrm{0}\:}\:\mathrm{applying}\:\mathrm{L}'\mathrm{Hopital}…
Question Number 129120 by liberty last updated on 13/Jan/21 $$\:\:\underset{\left({x},\mathrm{y}\right)\rightarrow\left(\infty,\infty\right)} {\mathrm{lim}}\left(\frac{\pi}{\mathrm{2}}\:−\mathrm{arctan}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)\right)^{\frac{\mathrm{1}}{\mathrm{ln}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)}} =? \\ $$ Answered by benjo_mathlover last updated on 13/Jan/21…
Question Number 129086 by Ar Brandon last updated on 12/Jan/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{x}}\mathrm{ln}\left(\frac{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}{\mathrm{x}}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 12/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{log}\left(\frac{{e}^{{x}}…
Question Number 128992 by liberty last updated on 12/Jan/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}\:\sqrt{\mathrm{x}−\mathrm{4}}\:−\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{5x}}\:\right)=? \\ $$ Answered by bramlexs22 last updated on 12/Jan/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{4x}^{\mathrm{2}} }\:−\sqrt{\mathrm{x}^{\mathrm{3}}…
Question Number 128908 by bramlexs22 last updated on 11/Jan/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:−\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{16}}\:\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 11/Jan/21 $$\left({x}^{\mathrm{2}} \sqrt{\mathrm{1}+\frac{\mathrm{4}}{{x}^{\mathrm{2}}…
Question Number 128846 by Ar Brandon last updated on 10/Jan/21 $$\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)\mathrm{sin}\left(\frac{\mathrm{k}}{\mathrm{n}^{\mathrm{2}} }\right) \\ $$$$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}u}_{\mathrm{n}} \\ $$ Commented by Dwaipayan Shikari last…
Question Number 128817 by benjo_mathlover last updated on 10/Jan/21 $$\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{ax}^{\mathrm{3}} +\mathrm{b}}\:−\mathrm{2x}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:=\:\mathrm{M}\:\mathrm{then}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{ax}^{\mathrm{3}} +\mathrm{b}}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2}}\:=? \\ $$ Answered by benjo_mathlover last updated on 10/Jan/21…
Question Number 128821 by benjo_mathlover last updated on 10/Jan/21 $$\:\mathrm{Nice}\:\mathrm{limit}\:! \\ $$$$\:\mathrm{For}\:−\mathrm{1}<{a}\:<\mathrm{1}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow−{a}} {\mathrm{lim}}\:\frac{\left({x}^{\mathrm{2}} +\mathrm{2}{ax}+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{ax}+{a}^{\mathrm{2}} \right)}{\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−{a}^{\mathrm{2}} }\:\right)^{\mathrm{2}} }\:=? \\ $$ Answered by liberty…