Question Number 207339 by Ghisom last updated on 12/May/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+{a}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+{b}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$ Answered by sniper237 last updated on 12/May/24 $$\:\frac{{a}}{{b}}\:\:\:{cause}\:\:\overset{{X}=\mathrm{1}/{x}}…
Question Number 206992 by mnjuly1970 last updated on 03/May/24 $$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mr W last updated on 03/May/24 $$−\mathrm{1}\leqslant{x}^{\mathrm{2}}…
Question Number 206934 by universe last updated on 01/May/24 Commented by Frix last updated on 01/May/24 $$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{sure},\:\mathrm{it}\:\mathrm{might}\:\mathrm{be}\:\:\sqrt[{\mathrm{e}}]{\mathrm{e}} \\ $$ Commented by universe last updated on…
Question Number 206730 by mathzup last updated on 23/Apr/24 $${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}}…