Question Number 130422 by john_santu last updated on 25/Jan/21 $$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\left(\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}^{\mathrm{5}} \right)}{\mathrm{tan}\:^{\mathrm{3}} \mathrm{3}{x}\:\left(\mathrm{5}^{{x}^{\mathrm{2}} } −\mathrm{1}\right)}\right)\:=? \\ $$ Answered by liberty last updated on 25/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 130406 by john_santu last updated on 25/Jan/21 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{cos}\:\left(\mathrm{2}{x}+\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}+{x}\right)=?\right. \\ $$ Commented by Dwaipayan Shikari last updated on 25/Jan/21 $$−\mathrm{1} \\ $$ Answered…
Question Number 130401 by john_santu last updated on 25/Jan/21 $${Where}\:{is}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)=\:\frac{\mathrm{ln}\:{x}+\mathrm{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} −\mathrm{1}}\:{continous}? \\ $$ Answered by mathmax by abdo last updated on 25/Jan/21…
Question Number 130223 by Study last updated on 23/Jan/21 $${li}\underset{{x}\rightarrow\overset{−} {\mathrm{5}}} {{m}lo}\underset{\frac{\mathrm{2}}{\mathrm{3}}} {{g}}\left(\mathrm{3}{x}−\mathrm{15}\right)=? \\ $$ Answered by EDWIN88 last updated on 23/Jan/21 $$\underset{{x}\rightarrow\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{log}\:_{\mathrm{2}/\mathrm{3}}…
Question Number 64671 by aliesam last updated on 20/Jul/19 Commented by mathmax by abdo last updated on 20/Jul/19 $${we}\:{have}\:\:\:{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\:\leqslant\:{sinx}\:\leqslant\:{x}\:\:\:{for}\:{all}\:{x}\:{real}\:\Rightarrow \\ $$$${n}^{\mathrm{2}} {x}−\frac{{n}^{\mathrm{6}} \:{x}^{\mathrm{3}} }{\mathrm{6}}\:\leqslant{sin}\left({n}^{\mathrm{2}}…
Question Number 130181 by Adel last updated on 23/Jan/21 Answered by Olaf last updated on 23/Jan/21 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\Gamma\left({x}+\mathrm{1}\right)−\mathrm{6}}{{xx}−\mathrm{33}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\Gamma\left({x}+\mathrm{1}\right)−\mathrm{6}}{\mathrm{11}\left({x}−\mathrm{3}\right)} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{3}}…
Question Number 64640 by Tawa1 last updated on 19/Jul/19 $$\mathrm{I}\:\:=\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\:\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{6n}\:+\:\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on 20/Jul/19 $${let}\:\:{S}\left({x}\right)\:=\sum_{{n}=\mathrm{0}}…
Question Number 130176 by liberty last updated on 23/Jan/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{6x}+\sqrt{\mathrm{8x}^{\mathrm{2}} −\sqrt{\mathrm{2x}^{\mathrm{3}} +\sqrt{\mathrm{4x}^{\mathrm{5}} }}}}{\:\sqrt[{\mathrm{6}}]{\mathrm{x}^{\mathrm{6}} −\mathrm{x}^{\mathrm{3}} +\sqrt{\mathrm{4x}^{\mathrm{5}} }}\:+\:\mathrm{x}}=? \\ $$ Answered by EDWIN88 last updated on…
Question Number 64612 by Tawa1 last updated on 19/Jul/19 Commented by Tawa1 last updated on 19/Jul/19 $$\mathrm{Just}\:\mathrm{the}\:\left(\mathrm{a}\right)\:\mathrm{part}\:\mathrm{please} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 130120 by Study last updated on 22/Jan/21 $${li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\sqrt{{x}−\mathrm{2}}=?\:\:\:\:{or}\:{limit}\:{has}? \\ $$ Answered by Olaf last updated on 22/Jan/21 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\sqrt{{x}−\mathrm{2}}\:\mathrm{is}\:\mathrm{undefined}…