Question Number 99968 by bobhans last updated on 24/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{x}\right)}} \:=?\: \\ $$ Commented by bobhans last updated on 24/Jun/20 $$=\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{ln}\left(\mathrm{x}\right)}} =\:\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}}…
Question Number 99951 by bemath last updated on 24/Jun/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4x}}\:+\:\mathrm{x}^{\mathrm{3}} \:? \\ $$ Commented by bobhans last updated on 24/Jun/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt{\mathrm{x}^{\mathrm{6}}…
Question Number 99947 by bemath last updated on 24/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}\right)\:=? \\ $$ Commented by bobhans last updated on 24/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} −\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{x}}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5}^{\mathrm{t}}…
Question Number 99935 by student work last updated on 24/Jun/20 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}} −\mathrm{1}\right)} }=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$ Commented by student work last updated on…
Question Number 99936 by student work last updated on 24/Jun/20 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{k}} −\mathrm{1}}{\mathrm{x}}=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$ Commented by bemath last updated on 24/Jun/20 $$\mathrm{for}\:\mathrm{k}\:>\:\mathrm{0}\:\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 99938 by bemath last updated on 24/Jun/20 $$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}+\sqrt{\mathrm{x}}−\mathrm{1}}{\:\sqrt{\mathrm{x}−\mathrm{1}}}\:?\: \\ $$ Commented by bobhans last updated on 24/Jun/20 $$\underset{\mathrm{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\frac{\mathrm{x}}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 34375 by rahul 19 last updated on 05/May/18 $$\boldsymbol{{T}}{he}\:{value}\:{of}\: \\ $$$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\:\:\frac{\left[\frac{{x}}{\mathrm{2}}\right]}{\mathrm{log}\:\left(\mathrm{sin}\:{x}\right)}\:=\:? \\ $$$$\left[.\right]=\:{greatest}\:{integer}\:{function}. \\ $$ Answered by MJS last updated on 05/May/18…
Question Number 34374 by rahul 19 last updated on 05/May/18 $${lim}_{{x}\rightarrow\mathrm{1}} \left\{\mathrm{1}−{x}+\left[{x}−\mathrm{1}\right]+\left[\mathrm{1}−{x}\right]\right\}\:=\:? \\ $$$$\left[.\right]=\:{greatest}\:{integer}\:{function}. \\ $$ Answered by MJS last updated on 05/May/18 $$\left[{x}−\mathrm{1}\right]=\left[{x}\right]−\mathrm{1} \\…
Question Number 34367 by rahul 19 last updated on 05/May/18 $$\boldsymbol{\mathrm{Evaluate}}\: \\ $$$$\mathrm{lim}_{\mathrm{n}\rightarrow\infty} \left(\frac{{n}}{{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }+\frac{{n}}{{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }+…..+\frac{{n}}{{n}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right). \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 99761 by Lekhraj last updated on 23/Jun/20 Commented by Dwaipayan Shikari last updated on 23/Jun/20 $${Ans}=\mathrm{1} \\ $$ Commented by Dwaipayan Shikari last…