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Category: Limits

lim-n-1-n-a-1-n-2-a-2-n-2-a-n-1-n-2-

Question Number 208093 by depressiveshrek last updated on 04/Jun/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\left(\left({a}+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} +\left({a}+\frac{\mathrm{2}}{{n}}\right)^{\mathrm{2}} +…+\left({a}+\frac{{n}−\mathrm{1}}{{n}}\right)^{\mathrm{2}} \right) \\ $$ Answered by MM42 last updated on 04/Jun/24 $$={lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\underset{{i}=\mathrm{1}}…

lim-x-2-x-2-4-1-3-x-3-4-x-2-4-x-2-1-3-

Question Number 207816 by efronzo1 last updated on 27/May/24 $$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}−\sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{4}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}−\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}} \\ $$ Commented by Frix last updated on 27/May/24 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\mathrm{0} \\…

lim-x-x-a-1-x-x-1-x-x-b-1-x-x-1-x-

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-206934

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…

lim-n-cosn-sinn-3-n-4-n-

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}…

let-f-0-R-be-a-continuous-function-if-lim-n-0-1-f-x-n-dx-2-then-lim-n-f-nx-

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…