Question Number 80650 by jagoll last updated on 05/Feb/20 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\left(\mid{x}\mid−{a}\right)^{\mathrm{3}} −\left(\mid{a}\mid−{a}\right)^{\mathrm{3}} }{{x}−{a}}\:=\:{P}\:,\:{a}\:<\mathrm{0} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{\left(\mid{x}\mid−{a}\right)^{\mathrm{2}} −\left(\mid{a}\mid−{a}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} −{ax}}=? \\ $$ Commented by john santu…
Question Number 146170 by EDWIN88 last updated on 11/Jul/21 $$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)\mathrm{tan}\:\left(\frac{\pi}{{x}}\right)=? \\ $$ Answered by iloveisrael last updated on 11/Jul/21 Answered by mathmax by…
Question Number 80614 by M±th+et£s last updated on 04/Feb/20 Commented by mathmax by abdo last updated on 04/Feb/20 $${A}_{{n}} =\frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{1}} ^{{n}} {ln}\left({a}+\frac{{k}}{{n}}\right)\Rightarrow{A}_{{n}} \:{is}\:{a}\:{Rieman}\:{sum} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty}…
Question Number 80586 by ahmadshahhimat775@gmail.com last updated on 04/Feb/20 Commented by kaivan.ahmadi last updated on 04/Feb/20 $${all}\:{are}\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 80585 by ahmadshahhimat775@gmail.com last updated on 04/Feb/20 Commented by kaivan.ahmadi last updated on 04/Feb/20 $$\mathrm{2}. \\ $$$${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{6}}} \:\frac{\mathrm{2}{sin}\mathrm{2}{x}+{cosx}}{\mathrm{2}{sin}\mathrm{2}{x}−\mathrm{3}{cosx}}=\frac{\sqrt{\mathrm{3}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}{\:\sqrt{\mathrm{3}}−\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}}=\frac{\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}}{\frac{−\sqrt{\mathrm{3}}}{\mathrm{2}}}=−\mathrm{3} \\ $$ Commented by kaivan.ahmadi…
Question Number 146119 by liberty last updated on 11/Jul/21 $$\:\:\:\:\:\:\:\:\:\begin{array}{|c|c|}{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{4}} }}{\mathrm{3}{x}}\:=?}\\{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{{x}^{\mathrm{6}} +\mathrm{3}{x}^{\mathrm{7}} }}\:=?}\\\hline\end{array} \\ $$ Commented by ajfour last updated on…
Question Number 146043 by liberty last updated on 10/Jul/21 Answered by iloveisrael last updated on 10/Jul/21 $$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} −\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\right)^{\mathrm{2}} } \\ $$$$\:\mathrm{let}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:=\:\mathrm{u}\:\rightarrow\mathrm{sin}\:\mathrm{x}=\mathrm{tan}\:\mathrm{u}\: \\…
Question Number 80455 by jagoll last updated on 03/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}+{mx}}{\mathrm{1}−{nx}}\right)^{\frac{{mn}}{{x}}} \\ $$ Commented by mr W last updated on 03/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}+{mx}}{\mathrm{1}−{nx}}\right)^{\frac{{mn}}{{x}}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 80442 by Power last updated on 03/Feb/20 Commented by john santu last updated on 03/Feb/20 $${f}\:'\left({a}\right)\:{hahaha} \\ $$ Commented by Power last updated…
Question Number 80417 by jagoll last updated on 03/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{{x}}} −{e}}{{x}}\:=\:? \\ $$ Commented by MJS last updated on 03/Feb/20 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{to}\:\mathrm{approximate}\:\mathrm{and}\:\mathrm{got}\:\mathrm{something} \\ $$$$\mathrm{very}\:\mathrm{close}\:\mathrm{to}\:−\frac{\mathrm{e}}{\mathrm{2}}\:\mathrm{but}\:\mathrm{I}\:\mathrm{cannot}\:\mathrm{prove}\:\mathrm{the} \\…