Question Number 96931 by bobhans last updated on 05/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{5x}^{\mathrm{4}} −\mathrm{8}}{\mathrm{7x}^{\mathrm{3}} +\mathrm{2}}×\mathrm{tan}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\:=? \\ $$ Commented by PRITHWISH SEN 2 last updated on 05/Jun/20 $$\underset{{x}\rightarrow\infty}…
Question Number 162398 by qaz last updated on 29/Dec/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{arctan}\:\left(\mathrm{t}+\mathrm{sin}\:\mathrm{x}\right)−\mathrm{arctan}\:\mathrm{t}\right)\mathrm{dt}}{\mathrm{arctan}\:\mathrm{x}}=? \\ $$ Answered by aleks041103 last updated on 29/Dec/21 $${both}\:{go}\:{to}\:\mathrm{0} \\ $$$${use}\:{l}'{hopital}…
Question Number 162399 by cortano last updated on 29/Dec/21 $$\:\:{Let}\:{m}\:\&\:{n}\:{be}\:{two}\:{positive}\:{numbers}\: \\ $$$$\:{greater}\:{than}\:\mathrm{1}\:.\:{If}\:\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{\mathrm{cos}\:\left({p}^{{n}} \right)} −{e}}{{p}^{{m}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}{e}\: \\ $$$$\:{then}\:\frac{{n}}{{m}}=? \\ $$ Commented by blackmamba last updated…
Question Number 162364 by cortano last updated on 29/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:{x}−\mathrm{sin}\:\mathrm{3}{x}\:\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{3}{x}\:\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$ Commented by blackmamba last updated on 29/Dec/21 $$\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:{x}−\mathrm{sin}\:\mathrm{5}{x}}{{x}^{\mathrm{3}} } \\…
Question Number 31246 by malwaan last updated on 04/Mar/18 $$\mathrm{without}\:\mathrm{using}\:\mathrm{lohpital} \\ $$$$\mathrm{find} \\ $$$$\underset{\mathrm{x}\rightarrow\pi/\mathrm{6}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2sinx}}{\mathrm{cos}\:\mathrm{3x}} \\ $$ Commented by malwaan last updated on 04/Mar/18 $$\mathrm{please}…
Question Number 162287 by qaz last updated on 28/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} }\mathrm{dx}=? \\ $$ Commented by mr W last updated on 28/Dec/21…
Question Number 96684 by Ar Brandon last updated on 03/Jun/20 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}+\mathrm{k}}{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} } \\ $$$$\left\{\mathrm{Reimann}'\mathrm{s}\:\:\mathrm{integral}\:\:\mathrm{may}\:\:\mathrm{help}\right\} \\ $$ Answered by Sourav mridha last…
Question Number 96685 by Ar Brandon last updated on 03/Jun/20 $$\underset{\omega\rightarrow\infty} {\mathrm{lim}20log}\sqrt{\mathrm{1}+\left(\frac{\omega}{\mathrm{100}}\right)^{\mathrm{2}} } \\ $$ Answered by Rio Michael last updated on 04/Jun/20 $$\mathrm{By}\:\mathrm{l}'\mathrm{hopitals}\:\mathrm{rule}\:\mathrm{i}\:\mathrm{get}\:+\infty\:\mathrm{as}\:\mathrm{answer} \\…
Question Number 162182 by bobhans last updated on 27/Dec/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2}}\:\right)^{\mathrm{2022}} +\left(\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{5}}\:\right)^{\mathrm{2022}} }{\mathrm{x}^{\mathrm{2022}} }\:=\:? \\ $$ Answered by cortano last updated on 27/Dec/21…
Question Number 96602 by Ar Brandon last updated on 03/Jun/20 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{k}} \\ $$ Answered by Sourav mridha last updated on 03/Jun/20 $$\boldsymbol{{by}}\:\boldsymbol{{inspection}}\:\underset{\boldsymbol{{k}}=\mathrm{1}}…