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Author: Tinku Tara

prove-that-9-4-lt-log-2-3-2-lt-25-9-

Question Number 11005 by ajfour last updated on 06/Mar/17 $${prove}\:{that}\:\frac{\mathrm{9}}{\mathrm{4}}\:<\:\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{3}\right)^{\mathrm{2}} \:<\:\frac{\mathrm{25}}{\mathrm{9}}\:\:. \\ $$ Answered by mrW1 last updated on 06/Mar/17 $$\mathrm{2log}_{\mathrm{2}} \:\mathrm{3}=\mathrm{log}_{\mathrm{2}} \:\mathrm{3}^{\mathrm{2}} =\mathrm{log}_{\mathrm{2}}…

Prove-that-3-gt-log-2-3-2-gt-2-

Question Number 10995 by Nadium last updated on 06/Mar/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{3}>\left(\mathrm{log}_{\mathrm{2}} \mathrm{3}\right)^{\mathrm{2}} >\mathrm{2}. \\ $$ Commented by FilupS last updated on 06/Mar/17 $$\mathrm{for}\:\:{l}=\mathrm{log}_{{n}} {x} \\ $$$$\mathrm{if}\:{n}>\mathrm{1}\:\mathrm{and}\:{x}\geqslant\mathrm{1},\:{l}\geqslant\mathrm{0}…

5x-2-y-2-z-2-2x-2-2xy-4xz-10-2x-y-13-3-

Question Number 142061 by iloveisrael last updated on 26/May/21 $$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}+\mathrm{2}{xy}−\mathrm{4}{xz}+\mathrm{10}}\:+ \\ $$$$\mid\mathrm{2}{x}−{y}−\mathrm{13}\mid\:=\:\mathrm{3}\: \\ $$ Commented by MJS_new last updated on 26/May/21 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}?…

Question-142060

Question Number 142060 by iloveisrael last updated on 26/May/21 Answered by Ar Brandon last updated on 26/May/21 $$\mathrm{I}=\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \mathrm{sec}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{tan}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{dx} \\ $$$${u}=\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \Rightarrow\mathrm{d}{u}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…

find-vector-unit-perpendicular-to-vector-a-1-2-3-and-b-1-0-2-

Question Number 76524 by john santu last updated on 28/Dec/19 $${find}\:{vector}\:{unit}\:{perpendicular}\: \\ $$$${to}\:{vector}\:\overset{−} {{a}}=\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\:{and}\:\overset{−} {{b}}=\left(−\mathrm{1},\mathrm{0},\mathrm{2}\right) \\ $$ Answered by MJS last updated on 28/Dec/19 $$\begin{vmatrix}{\mathrm{1}}&{−\mathrm{1}}&{{u}_{{x}}…