Question Number 63920 by raj last updated on 11/Jul/19 $$\mathrm{If}\:\alpha,\beta\:\mathrm{are}\:\mathrm{root}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}\:\mathrm{then} \\ $$$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left({ax}^{\mathrm{2}} +{bx}+{c}\right)}{\left({x}−\alpha\right)^{\mathrm{2}} }=? \\ $$ Commented by Prithwish sen last…
Question Number 63918 by raj last updated on 11/Jul/19 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\frac{\left[\mathrm{1}−\mathrm{tan}\:{x}/\mathrm{2}\right]\left[\mathrm{1}−\mathrm{sin}\:{x}\right]}{\left[\mathrm{1}+\mathrm{tan}\:{x}/\mathrm{2}\right]\left[\pi−\mathrm{2}{x}\right]^{\mathrm{3}} }=? \\ $$ Answered by Cmr 237 last updated on 20/Aug/19 $${posons}\:{cette}\:{limite}\:{egale}\:{A} \\ $$$${par}\:{le}\:{developement}\:{limite}\:{we}\:{have}:…
Question Number 129387 by Study last updated on 15/Jan/21 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left({cosx}\right)^{{logx}} =??? \\ $$ Commented by Study last updated on 15/Jan/21 $${who}\:{will}\:{solve}? \\ $$ Answered…
Question Number 129385 by Adel last updated on 15/Jan/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}\:}}\frac{\:}{\:\sqrt{\mathrm{n}+\mathrm{1}}}+\frac{\:}{\:\sqrt{\mathrm{n}}}\frac{\:\mathrm{1}}{\:\sqrt{\mathrm{n}+\mathrm{2}}}\frac{\:}{\:}+\frac{\:}{\:\sqrt{\boldsymbol{\mathrm{n}}}}\frac{\:}{\:\sqrt{\boldsymbol{\mathrm{n}}+\mathrm{3}}}\frac{\mathrm{1}}{\:}\frac{\:}{\:}+…………..+\frac{\:}{\:\sqrt{\mathrm{n}}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}+\mathrm{n}}}\frac{\:}{\:}=? \\ $$$$\:{what}\:{answer} \\ $$ Answered by Dwaipayan Shikari last updated on 15/Jan/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}}…
Question Number 63710 by aliesam last updated on 07/Jul/19 Commented by mathmax by abdo last updated on 08/Jul/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{{n}}} {n}^{\mathrm{2}} \:{x}^{{x}+\mathrm{1}} \:{ex}\:\Rightarrow{A}_{{n}} =\int_{\mathrm{0}}…
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}}…