Question Number 160244 by cortano last updated on 26/Nov/21 $$\:\:\:\:\:{L}\underset{{x}\rightarrow\mathrm{0}} {{i}m}\:\left(\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)−\mathrm{tan}\:\left({x}\right)}{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−\mathrm{sin}\:\left({x}\right)}\right)=? \\ $$ Answered by FongXD last updated on 26/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}−\mathrm{tanx}}{\mathrm{x}^{\mathrm{3}}…
Question Number 160241 by mathlove last updated on 26/Nov/21 Commented by blackmamba last updated on 26/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{9}}]{\mathrm{7}{x}−\mathrm{6}}−\mathrm{1}}{{nx}^{\mathrm{3}} −{n}}\: \\ $$$$\:\:\:\:\:=\:\frac{\mathrm{1}}{{n}}\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{9}}]{\mathrm{7}{x}−\mathrm{6}}−\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)} \\ $$$$\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{3}{n}}\:\underset{{x}\rightarrow\mathrm{1}}…
Question Number 29158 by abdo imad last updated on 04/Feb/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \frac{\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}}{\:\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}}\:\:. \\ $$ Commented by abdo imad last updated on 09/Feb/18 $${in}\:{this}\:{case}\:{its}\:{better}\:{to}\:{use}\:{hospital}\:{theorem}\:{let}\:{put} \\ $$$${u}\left({x}\right)=\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}\:{and}\:{v}\left({x}\right)=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}…
Question Number 29157 by abdo imad last updated on 04/Feb/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\frac{\left({x}−\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:\:+\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{{x}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 160218 by qaz last updated on 26/Nov/21 $$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{arctan}\:\mathrm{t}\right)^{\mathrm{2}} \mathrm{dt}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}=? \\ $$ Answered by mathmax by abdo last updated on…
Question Number 94679 by i jagooll last updated on 20/May/20 Commented by i jagooll last updated on 20/May/20 $$\mathrm{dear}\:\mathrm{tinkutara}\:\mathrm{sir}\:\mathrm{how}\:\mathrm{my}\:\mathrm{image}\:\mathrm{post}? \\ $$ Commented by i jagooll…
Question Number 160178 by cortano last updated on 25/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)−\mathrm{1}}\:=? \\ $$ Commented by blackmamba last updated on 25/Nov/21 $$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)−\mathrm{1}}\: \\ $$$$\:\:\:\:\:\:\:=\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{1}}{−\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 160142 by cortano last updated on 25/Nov/21 Answered by puissant last updated on 25/Nov/21 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}^{\mathrm{1111}} +\mathrm{2}{x}^{\mathrm{2222}} −\mathrm{3}{x}^{\mathrm{3333}} }{{x}^{\mathrm{4444}} −\mathrm{1}}\: \\ $$$$=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\frac{{d}}{{dx}}\left\{{x}^{\mathrm{1111}}…
Question Number 160080 by qaz last updated on 24/Nov/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}−\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}}{\mathrm{x}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}=? \\ $$ Answered by mr W last updated on 25/Nov/21…
Question Number 160077 by qaz last updated on 24/Nov/21 $$\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\frac{\mathrm{654}}{\mathrm{1}−\mathrm{x}^{\mathrm{654}} }−\frac{\mathrm{678}}{\mathrm{1}−\mathrm{x}^{\mathrm{678}} }\right)=? \\ $$ Commented by cortano last updated on 25/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{654}}{\mathrm{1}−{x}^{\mathrm{654}} }\:−\:\frac{\mathrm{678}}{\mathrm{1}−{x}^{\mathrm{678}}…