Menu Close

Category: Limits

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}…

L-lim-x-1-2019x-2018-1-x-2019-1-2018-1-then-2-L-

Question Number 153517 by liberty last updated on 08/Sep/21 $$\:\:{L}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2019}{x}−\mathrm{2018}}−\mathrm{1}}{\:\sqrt[{\mathrm{2018}}]{{x}^{\mathrm{2019}} }−\mathrm{1}} \\ $$$$\:{then}\:\mathrm{2}×{L}\:=? \\ $$ Commented by MJS_new last updated on 08/Sep/21 $$\mathrm{just}\:“\mathrm{hospitalize}''\:\mathrm{it}\:\Rightarrow\:{L}=\mathrm{1009} \\…

Show-whether-n-1-x-2-3-n-2-x-2-is-uniformly-convegence-for-real-value-of-x-

Question Number 153518 by Tawa11 last updated on 08/Sep/21 $$\mathrm{Show}\:\mathrm{whether}\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{3}\:\:\:\:+\:\:\:\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\right)\:\:\:\:\:\mathrm{is}\:\mathrm{uniformly}\:\mathrm{convegence}\:\mathrm{for}\:\mathrm{real} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by puissant last updated on…