Question Number 206730 by mathzup last updated on 23/Apr/24 $${find}\:{lim}_{{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{{n}} {e}^{{nx}} \:{arctan}\left(\frac{{x}}{{n}}\right){dx} \\ $$ Commented by aleks041103 last updated on 24/Apr/24 $${More}\:{interesting}\:{is} \\…
Question Number 206702 by depressiveshrek last updated on 22/Apr/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{cos}{n}+\mathrm{sin}{n}−\mathrm{3}^{{n}} +\mathrm{4}^{{n}} } \\ $$ Answered by Frix last updated on 22/Apr/24 $$−\sqrt{\mathrm{2}}\leqslant\mathrm{cos}\:{n}\:+\mathrm{sin}\:{n}\:\leqslant\sqrt{\mathrm{2}} \\ $$$$\forall{a}\in\mathbb{R}:\underset{{n}\rightarrow\infty}…
Question Number 206669 by depressiveshrek last updated on 21/Apr/24 $$\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{2}}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{20}}}{\:\sqrt[{\mathrm{4}}]{{x}+\mathrm{9}}−\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 206433 by universe last updated on 14/Apr/24 $$\:\:\:\:\:\mathrm{let}\:\mathrm{f}:\left[\mathrm{0},\infty\right)\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{if} \\ $$$$\:\:\:\:\underset{\mathrm{n}\rightarrow\infty\:} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}+\mathrm{n}\right)\mathrm{dx}\:=\:\mathrm{2} \\ $$$$\:\mathrm{then}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{nx}\right)\:=\:? \\ $$$$\: \\ $$ Answered by Berbere…
Question Number 206069 by MathematicalUser2357 last updated on 06/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{3}} +{x}}{\mathrm{sin}\:{x}} \\ $$ Answered by MetaLahor1999 last updated on 06/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−{x}^{\mathrm{3}} }{{sin}\left({x}\right)}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 206095 by RoseAli last updated on 06/Apr/24 Answered by Frix last updated on 07/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{sin}\:{x}}{{x}−\mathrm{tan}\:{x}}\:\:\overset{\left[\mathrm{l}'\mathrm{H}\hat {\mathrm{o}pital}\right]} {=}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{{d}}{{dx}}\left[{x}−\mathrm{sin}\:{x}\right]}{\frac{{d}}{{dx}}\left[{x}−\mathrm{tan}\:{x}\right]}\:= \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{−\mathrm{tan}^{\mathrm{2}} \:{x}}…
Question Number 205916 by mathzup last updated on 02/Apr/24 $${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{xln}\left({e}^{{x}} −\mathrm{1}\right) \\ $$ Answered by mathzup last updated on 03/Apr/24 $${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{xln}\left({e}^{{x}}…
Question Number 205774 by mnjuly1970 last updated on 30/Mar/24 $$ \\ $$$$\:\:\:\:\:\:−−−−−−− \\ $$$$\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}} }{\left(−\mathrm{1}\right)^{\:{n}} \:−{n}}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:−−−−−−− \\ $$ Answered by MathedUp…
Question Number 205716 by universe last updated on 28/Mar/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)…\left(\mathrm{4}{n}+\mathrm{1}\right)}{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)…\left(\mathrm{4}{n}\right)}\:\:=\:\:? \\ $$ Answered by MM42 last updated on 28/Mar/24 $$\frac{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)…\left(\mathrm{4}{n}\right)}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)…\left(\mathrm{4}{n}−\mathrm{1}\right)}<{A}<\frac{\left(\mathrm{2}{n}+\mathrm{2}\right)\left(\mathrm{2}{n}+\mathrm{4}\right)…\left(\mathrm{4}{n}+\mathrm{2}\right)}{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)…\left(\mathrm{4}{n}+\mathrm{1}\right)} \\ $$$$\Rightarrow\frac{\mathrm{4}{n}+\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right){A}}<{A}<\frac{\mathrm{4}{n}+\mathrm{2}}{\left(\mathrm{2}{n}\right){A}} \\ $$$$\Rightarrow\frac{\mathrm{4}{n}+\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}<{A}^{\mathrm{2}}…
Question Number 205727 by mathzup last updated on 28/Mar/24 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{e}^{{x}} −{cosx}}{{x}^{\mathrm{2}} } \\ $$ Commented by lepuissantcedricjunior last updated on 29/Mar/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}} −\boldsymbol{{cosx}}}{\boldsymbol{{x}}^{\mathrm{2}}…