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Category: Limits

Question-154292

Question Number 154292 by mnjuly1970 last updated on 16/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 16/Sep/21 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{3}\centerdot\mathrm{5}\centerdot\centerdot\centerdot\left(\mathrm{2}{n}+\mathrm{1}\right)}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}\left(\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{6}\centerdot\centerdot\centerdot\mathrm{2}{n}\right)}{\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}\centerdot\mathrm{5}\centerdot\mathrm{6}\centerdot\centerdot\centerdot\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$$$\:\:\:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{{n}}…

The-x-n-sequence-is-specified-by-the-conditions-x-1-1982-x-n-1-1-4-x-n-n-0-find-lim-n-x-n-

Question Number 154252 by EDWIN88 last updated on 16/Sep/21 $$\:\:{The}\:\left\{{x}_{{n}} \right\}\:{sequence}\:{is}\:{specified} \\ $$$$\:{by}\:{the}\:{conditions}\: \\ $$$$\:\:\begin{cases}{{x}_{\mathrm{1}} =\mathrm{1982}}\\{{x}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{4}−{x}_{{n}} },{n}\geqslant\mathrm{0}}\end{cases} \\ $$$$\:{find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{x}_{{n}} . \\ $$ Terms…

lim-x-0-1-4x-1-6x-1-3-1-cos-3x-

Question Number 88580 by jagoll last updated on 11/Apr/20 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{4x}}\:−\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{6x}}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}}\:= \\ $$ Commented by mathmax by abdo last updated on 11/Apr/20 $${let}\:{f}\left({x}\right)=\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}}−^{\mathrm{3}}…

Question-23012

Question Number 23012 by A1B1C1D1 last updated on 25/Oct/17 Commented by ajfour last updated on 25/Oct/17 $${i}\:{had}\:{solved}\:{your}\:{previous}\: \\ $$$${question}\:\int_{\mathrm{0}} ^{\:\:\mathrm{2}} \int_{{y}/\mathrm{2}} ^{\:\:\mathrm{1}} {e}^{{x}^{\mathrm{2}} } {dxdy}\:=?…

lim-x-32x-5-14x-4-3-1-5-128x-7-6x-6-1-1-7-

Question Number 154081 by iloveisrael last updated on 14/Sep/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\mathrm{5}}]{\mathrm{32}{x}^{\mathrm{5}} −\mathrm{14}{x}^{\mathrm{4}} +\mathrm{3}}−\sqrt[{\mathrm{7}}]{\mathrm{128}{x}^{\mathrm{7}} +\mathrm{6}{x}^{\mathrm{6}} −\mathrm{1}}\:=? \\ $$ Answered by EDWIN88 last updated on 14/Sep/21 $$\:\underset{{x}\rightarrow\infty}…

lim-x-pi-2-1-sec-2-x-2-sec-2-x-3-sec-2-x-n-sec-2-x-cos-2-x-

Question Number 22947 by ajfour last updated on 26/Oct/17 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\left(\mathrm{1}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{2}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{3}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +….\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…+{n}^{\mathrm{sec}\:^{\mathrm{2}} {x}} \right)^{\mathrm{cos}\:^{\mathrm{2}} {x}} \:=\:? \\ $$$$…

Question-88288

Question Number 88288 by Chi Mes Try last updated on 09/Apr/20 Commented by abdomathmax last updated on 10/Apr/20 $${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{sin}\left({ln}\mid{x}\mid\right)}{{ln}\mid{x}\mid}{dx}\:\:{changement}\:\:{ln}\left({x}\right)=−{u}\:\Rightarrow \\ $$$${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left({lnx}\right)}{{lnx}}{dx}\:=−\int_{\mathrm{0}}…

Given-f-R-R-is-increasing-positive-function-with-lim-x-f-3x-f-x-1-What-the-value-of-lim-x-f-2x-f-x-A-3-B-3-2-C-1-D-2-3-E-

Question Number 153765 by liberty last updated on 10/Sep/21 $$\:{Given}\:{f}:{R}\rightarrow{R}\:{is}\:{increasing}\:{positive} \\ $$$${function}\:{with}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{f}\left(\mathrm{3}{x}\right)}{{f}\left({x}\right)}=\mathrm{1}\:.\: \\ $$$${What}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{f}\left(\mathrm{2}{x}\right)}{{f}\left({x}\right)}. \\ $$$$\left({A}\right)\:\mathrm{3}\:\:\:\:\:\left({B}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\left({C}\right)\:\mathrm{1}\:\:\:\:\:\left({D}\right)\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\left({E}\right)\:\infty \\ $$ Answered by gsk2684 last updated…