Question Number 120686 by bobhans last updated on 01/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:? \\ $$ Answered by john santu last updated on 02/Nov/20 $${standart}\:{way}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 55149 by pooja24 last updated on 18/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 18/Feb/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{li}} \\ $$$${x}={tan}\theta\:\:\:\:{as}\:{x}\rightarrow\mathrm{0}\:\:\theta\rightarrow\mathrm{0} \\ $$$$\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{ln}\left({tan}\theta+{sec}\theta\right)}−\frac{\mathrm{1}}{{ln}\left(\mathrm{1}−{tan}\theta\right)} \\ $$$$\underset{\theta\rightarrow\mathrm{0}}…
Question Number 186065 by TUN last updated on 31/Jan/23 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{7}{x}^{\mathrm{2}} +\mathrm{10}{x}+\mathrm{9}}−\sqrt{\mathrm{6}{x}+\mathrm{3}}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by Frix last updated on 01/Feb/23…
Question Number 186064 by TUN last updated on 31/Jan/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left({cos}\mathrm{2}{x}\:−{cos}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{10}}\right) \\ $$$$ \\ $$ Commented by a.lgnaoui last updated on 31/Jan/23 $$\mathrm{2}{x}={t}\:\:\: \\…
Question Number 186066 by TUN last updated on 31/Jan/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{7}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{2}}−{x}+\mathrm{1}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} }\right) \\ $$$$ \\ $$ Answered by…
Question Number 54992 by Mikael_Marshall last updated on 15/Feb/19 $$\underset{{n}\rightarrow\infty} {{lim}}\left(\sqrt{{n}^{\mathrm{3}} +{n}^{\mathrm{2}} +{n}+\mathrm{1}}−{n}\right) \\ $$ Answered by kaivan.ahmadi last updated on 15/Feb/19 $$×\frac{\sqrt{{n}^{\mathrm{3}} +{n}^{\mathrm{2}} +{n}+\mathrm{1}}+{n}}{\:\sqrt{{n}^{\mathrm{3}}…
Question Number 120515 by john santu last updated on 01/Nov/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{3}\:\sqrt[{{x}\:}]{\mathrm{2}}\:−\mathrm{2}.\sqrt[{{x}\:}]{\mathrm{3}}\:\right)^{{x}} \:? \\ $$ Answered by bramlexs22 last updated on 01/Nov/20 $$\mathrm{ln}\:\mathrm{L}\:=\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{3}.\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{x}}} \:−\mathrm{2}.\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{x}}}…
Question Number 120511 by bramlexs22 last updated on 01/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\left[\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)\right]^{\mathrm{3}} }}{{x}\:\mathrm{sin}\:\left(\sqrt{{x}}\right)}\:?\: \\ $$ Answered by Olaf last updated on 01/Nov/20 $$\frac{\sqrt{\mathrm{arcsin}^{\mathrm{3}} \left(\mathrm{2}{x}\right)}}{{x}\mathrm{sin}\left(\sqrt{{x}}\right)}\:\underset{\mathrm{0}^{+} }…
Question Number 120427 by bramlexs22 last updated on 31/Oct/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{cos}\:{x}+\sqrt{\mathrm{2sin}\:{x}+{x}}}\:−\mathrm{1}}{\mathrm{sin}\:{x}} \\ $$ Answered by john santu last updated on 31/Oct/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{cos}\:{x}+\sqrt{\mathrm{2sin}\:{x}+{x}}}−\mathrm{1}}{\mathrm{sin}\:{x}}\:= \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 120425 by bobhans last updated on 31/Oct/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{{x}} −\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\:? \\ $$ Answered by john santu last updated on 31/Oct/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{{x}} −\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}}…