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Category: Limits

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…

lim-x-cos-npi-e-1-2n-

Question Number 153598 by liberty last updated on 08/Sep/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}cos}\:\left({n}\pi\:\sqrt[{\mathrm{2}{n}}]{{e}}\:\right)=? \\ $$ Commented by tabata last updated on 08/Sep/21 $$\boldsymbol{{y}}=\:\boldsymbol{{n}\pi}\:\sqrt[{\mathrm{2}\boldsymbol{{n}}}]{\boldsymbol{{e}}}\: \\ $$$$ \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{y}}\rightarrow\infty}…