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…
Question Number 63190 by Tawa1 last updated on 30/Jun/19 $$\mathrm{Test}\:\mathrm{its}\:\mathrm{convergence}:\:\:\:\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \:\mathrm{sin}^{\mathrm{2}} \mathrm{n}} \\ $$ Commented by mathmax by abdo last updated on 01/Jul/19…
Question Number 128674 by bemath last updated on 09/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4x}−\mathrm{12tan}\:\mathrm{x}}{\mathrm{3sin}\:\mathrm{4x}−\mathrm{12sin}\:\mathrm{x}}\:=\:? \\ $$$$ \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\mathrm{Taylor}\:\mathrm{series}\:\begin{cases}{\mathrm{tan}\:\mathrm{x}=\mathrm{x}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{2x}^{\mathrm{5}} }{\mathrm{15}}+…}\\{\mathrm{tan}\:\mathrm{4x}=\mathrm{4x}+\frac{\mathrm{64x}^{\mathrm{3}}…
Question Number 128654 by john_santu last updated on 09/Jan/21 $$\:\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\:\:\left[\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:\mathrm{x}}\:−\mathrm{1}}{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}\:\right]\:=? \\ $$ Answered by bemath last updated on 09/Jan/21 Terms of Service Privacy…
Question Number 128626 by john_santu last updated on 09/Jan/21 $$\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left\{\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\mathrm{n}} \right\}=? \\ $$$$\left\{\:\right\}\:=\:\mathrm{fractional}\: \\ $$$$ \\ $$ Commented by liberty last updated on 09/Jan/21…
Question Number 128624 by john_santu last updated on 09/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mid\mathrm{x}^{\mathrm{2}} +\mathrm{1}\mid−\mid\mathrm{x}^{\mathrm{2}} −\mathrm{1}\mid}{\mid\mathrm{2000x}+\mathrm{5}\mid−\mid\mathrm{2000x}−\mathrm{5}\mid}\:=? \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)+\left(\mathrm{x}^{\mathrm{2}}…