Question Number 130596 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{equation}\:\mathrm{true}?\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{a}\:+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{2}} }\:\right)=\:\mathrm{0}. \\ $$ Answered by mr W last updated…
Question Number 130559 by Ar Brandon last updated on 26/Jan/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\mathrm{2xsin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\right\} \\ $$ Answered by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{no}\:\mathrm{limit} \\…
Question Number 130541 by EDWIN88 last updated on 26/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{−{x}^{\mathrm{2}} /\mathrm{2}} −\mathrm{cos}\:{x}}{{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 130508 by Raxreedoroid last updated on 26/Jan/21 $${lim}\:_{{n}\rightarrow\infty} \underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{cos}\left({x}\centerdot{ln}\left({k}\right)\right)}{\:\sqrt{{k}}}=? \\ $$$${where}\:{x}\in\mathbb{R} \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21…
Question Number 130483 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 10/Feb/21 $$\left(\mathrm{5}\right)\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}cos}\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{cos}\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}f}\left(\mathrm{x}\right)=\mathrm{cos}\:\left(−\mathrm{1}\right)=\mathrm{cos}\:\mathrm{1} \\ $$ Terms of Service Privacy…
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}}…