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Author: Tinku Tara

x-3-1-2-2x-1-1-3-

Question Number 140669 by john_santu last updated on 11/May/21 $$\:{x}^{\mathrm{3}} +\mathrm{1}\:=\:\mathrm{2}\:\sqrt[{\mathrm{3}\:}]{\mathrm{2}{x}−\mathrm{1}} \\ $$ Answered by bemath last updated on 11/May/21 $$\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}{\mathrm{2}}\:=\:\sqrt[{\mathrm{3}\:}]{\mathrm{2x}−\mathrm{1}} \\ $$$$\:\mathrm{set}\:\mathrm{g}\left(\mathrm{x}\right)=\:\sqrt[{\mathrm{3}\:}]{\mathrm{2x}−\mathrm{1}}\:\Rightarrow\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}{\mathrm{2}}\:=\:\mathrm{g}^{−\mathrm{1}}…

calculus-II-find-convergence-of-n-2-1-n-ln-3-n-ln-n-

Question Number 140671 by mnjuly1970 last updated on 11/May/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:……\:{calculus}\:….\:\left({II}\right)….. \\ $$$$\:\:\:{find}\:{convergence}\:{of}\::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}\left({ln}^{\mathrm{3}} \left({n}\right)+{ln}\left({n}\right)\right)}\: \\ $$$$ \\ $$ Answered by…

dx-x-x-6-x-3-1-

Question Number 140665 by ERA last updated on 11/May/21 $$\int\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{6}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}}} \\ $$ Answered by MJS_new last updated on 11/May/21 $$\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{6}} +{x}^{\mathrm{3}} +\mathrm{1}}}= \\…

please-help-me-to-show-that-tan-2-pi-8-2tan-pi-8-1-0-

Question Number 75131 by mathocean1 last updated on 07/Dec/19 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{2tan}\left(\frac{\pi}{\mathrm{8}}\right)−\mathrm{1}=\mathrm{0} \\ $$ Answered by mr W last updated on 07/Dec/19 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=\mathrm{1} \\…

Find-the-coordinates-of-2-0-when-the-axes-are-rotated-counterclockwise-through-the-angle-arcsin-4-5-

Question Number 140666 by john_santu last updated on 11/May/21 $${Find}\:{the}\:{coordinates}\:{of}\:\left(−\mathrm{2},\mathrm{0}\right)\: \\ $$$${when}\:{the}\:{axes}\:{are}\:{rotated}\:{counterclockwise} \\ $$$${through}\:{the}\:{angle}\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}. \\ $$ Answered by bemath last updated on 11/May/21 $$\begin{cases}{\mathrm{x}'=\mathrm{x}\:\mathrm{cos}\:\theta−\mathrm{ysin}\:\theta}\\{\mathrm{y}'=\mathrm{xsin}\:\theta+\mathrm{ycos}\:\theta}\end{cases} \\…