Question Number 190824 by cortano12 last updated on 12/Apr/23 $$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}\sqrt{\mathrm{tan}\:\mathrm{x}}}{\mathrm{2cos}\:\mathrm{x}−\mathrm{2sin}\:\mathrm{x}}\:=? \\ $$ Commented by 0670322918 last updated on 12/Apr/23 $$\frac{\mathrm{1}}{\mathrm{2}}\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{{tan}^{\mathrm{2}} \left({x}\right)+\mathrm{1}−\mathrm{2}+\mathrm{2}−\mathrm{2}\sqrt{{tan}\left({x}\right)}}{{cos}\left({x}\right)\left[\mathrm{1}−{tan}\left({x}\right)\right]}= \\…
Question Number 125292 by Kurbanklichevs last updated on 09/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({x}+\mathrm{1}\right)^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right)\left({x}+\mathrm{1}\right)+{n}}{{x}^{\mathrm{2}} }\:\:\:\:\:{n}\in\mathbb{N} \\ $$$${Calculate}.\:\left({Without}\:{a}\:{L}'{Hopital}'{s}\:{rule}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 09/Dec/20…
Question Number 125282 by Mammadli last updated on 09/Dec/20 $$\mathrm{1}.\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt[{\boldsymbol{{n}}}]{\frac{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}}{\mathrm{2}\boldsymbol{{n}}+\mathrm{1}}}=? \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\sqrt[{\boldsymbol{{n}}}]{\frac{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}}{\mathrm{2}\boldsymbol{{n}}+\mathrm{1}}}=? \\ $$ Answered by mathmax by abdo last updated on…
Question Number 190788 by mnjuly1970 last updated on 11/Apr/23 $$ \\ $$$$\:\:\:\:\mathrm{calculate}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\Omega=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\:\mathrm{1}}{\left({n}−{k}\right)!.\left({n}+{k}\:\right)!} \\ $$$$ \\ $$ Answered by aleks041103…
Question Number 59694 by meme last updated on 13/May/19 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{cos}\left(\sqrt{\left.\mid{x}\mid\right)−\mathrm{1}}\right.}{{x}}=? \\ $$ Commented by maxmathsup by imad last updated on 13/May/19 $${let}\:{A}\left({x}\right)\:=\frac{{cos}\left(\sqrt{\mid{x}\mid}\right)−\mathrm{1}}{{x}}\:\:\:\:{we}\:{have}\:{cos}\left({u}\right)\:\sim\mathrm{1}−\frac{{u}^{\mathrm{2}} }{\mathrm{2}}\:\left(\:\:{u}\in{V}\left(\mathrm{0}\right)\right)\:\Rightarrow \\…
Question Number 125204 by bemath last updated on 09/Dec/20 Answered by liberty last updated on 09/Dec/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{3}^{\mathrm{4}{x}} \right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} \:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}{x}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} =\: \\ $$$$\:\mathrm{9}\:×\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}{x}}…
Question Number 59637 by mathtype last updated on 12/May/19 $$\underset{{x}\rightarrow\infty} {{lim}}\frac{\mathrm{1}}{{x}}\int_{\mathrm{0}} ^{{x}} \mid\mathrm{sin}\:{x}\mid \\ $$ Commented by Mr X pcx last updated on 13/May/19 $${there}\:{is}\:{a}\:{problem}\:{here}\:{let}\:{take}\:{x}={n}\pi…
Question Number 190679 by mathlove last updated on 09/Apr/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{e}^{{x}} }{{x}^{\mathrm{60}!} }=? \\ $$$${pleas}\:{solve}\:{this} \\ $$ Answered by Frix last updated on 09/Apr/23 $$\frac{\mathrm{e}^{{x}}…
Question Number 59599 by tanmay last updated on 12/May/19 Answered by tanmay last updated on 12/May/19 $${T}_{{r}} =\frac{{tan}\frac{{x}}{\mathrm{2}^{{r}+\mathrm{1}} }\left(\mathrm{1}+{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{r}+\mathrm{1}} }\right)}{\mathrm{1}−{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{r}+\mathrm{1}} }} \\ $$$${T}_{{r}}…
Question Number 59542 by Mikael_Marshall last updated on 11/May/19 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\mathrm{ln}\left(\mathrm{cosx}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$$${I}\:{have}\:{a}\:{doubt} \\ $$ Commented by kaivan.ahmadi last updated on 11/May/19 $${hop} \\…