Question Number 31529 by abdo imad last updated on 09/Mar/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}^{−} } \:\:\:\:{lnx}.{ln}\left(\mathrm{1}−{x}\right)\:. \\ $$ Commented by abdo imad last updated on 11/Mar/18 $${lim}_{{x}\rightarrow\mathrm{1}^{−} }…
Question Number 31528 by abdo imad last updated on 09/Mar/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{2}} \:\:\frac{{x}^{\mathrm{2}} \:\:−\mathrm{2}^{{x}} }{{arctanx}\:−{artan}\mathrm{2}}\:. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{put}\:{f}\left({x}\right)=\mathrm{2}^{{x}}…
Question Number 31524 by abdo imad last updated on 09/Mar/18 $${find}\:{lim}_{{n}\rightarrow\infty} \left(\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)^{{n}} . \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{put}\:{A}_{{n}} \:=\left(\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)^{{n}}…
Question Number 31522 by abdo imad last updated on 09/Mar/18 $${let}\:{give}\:{u}_{{n}} =\sqrt{{ln}\left({n}+\mathrm{1}\right)−{ln}\left({n}\right)}\: \\ $$$$\left.\mathrm{1}\right){give}\:{a}\:{simple}\:{eqivalent}\:{of}\:{u}_{{n}} \:\left({n}\rightarrow\infty\right) \\ $$$$\left.\mathrm{2}\right)\:{deduce}\:{the}\:{nature}\:{of}\:{u}_{{n}} . \\ $$ Commented by abdo imad last…
Question Number 162585 by qaz last updated on 30/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2n}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\right)^{\mathrm{n}} =? \\ $$ Answered by mathmax by abdo last updated…
Question Number 31511 by abdo imad last updated on 09/Mar/18 $${f}\:{is}\:{C}^{\mathrm{2}} \:{inside}\:{R}\:{and}\:{a}\in{R}\:{find} \\ $$$${lim}_{{h}\rightarrow\mathrm{0}} \:\frac{\left.{fa}+{h}\right)−\mathrm{2}{f}\left({a}\right)\:+{f}\left({a}−{h}\right)}{{h}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31461 by abdo imad last updated on 08/Mar/18 $${let}\:{give}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\:\left(\frac{{k}}{{n}}\right)\:{sin}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{is}\:{convergent} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} . \\ $$ Terms…
Question Number 162523 by cortano last updated on 30/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7tan}\:{x}−\mathrm{tan}\:\mathrm{7}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by Ar Brandon last updated on 30/Dec/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{7tan}{x}−\mathrm{tan7}{x}}{{x}^{\mathrm{3}} }…
Question Number 96977 by 175 last updated on 05/Jun/20 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{{x}\:−\:\mathrm{5}}{\mathrm{2}\:+\:\mathrm{cot}^{\mathrm{2}} \frac{\mathrm{2}}{{x}\:−\mathrm{5}}} \\ $$ Answered by mathmax by abdo last updated on 06/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}−\mathrm{5}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{2}}{\mathrm{x}−\mathrm{5}}\right)}}\:\:\mathrm{changement}\:\mathrm{x}−\mathrm{5}\:=\mathrm{t}\:\mathrm{give}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{t}\right)…
Question Number 162510 by cortano last updated on 30/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7tan}\:{x}−\mathrm{tan}\:\mathrm{7}{x}}{\mathrm{3}{x}}\:=? \\ $$ Answered by Lordose last updated on 30/Dec/21 $$\mathrm{L}−\mathrm{Hopital}'\mathrm{s};\:\frac{\mathrm{7sec}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{7sec}^{\mathrm{2}} \left(\mathrm{7x}\right)}{\mathrm{3}}\:=\:\frac{\mathrm{0}}{\mathrm{3}}\:=\:\mathrm{0} \\ $$…