Question Number 75224 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{xln}\mid\mathrm{x}\mid−\left(\mathrm{x}−\mathrm{m}\right)\mathrm{ln}\mid\mathrm{x}−\mathrm{m}\mid\right)=+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75228 by ~blr237~ last updated on 08/Dec/19 $$\:\mathrm{Let}\:\mathrm{consider}\: \\ $$$$\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \left(\Gamma\left(\mathrm{t}\right)\right)^{\mathrm{x}} \mathrm{dt}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\Gamma\left(\mathrm{t}\right)\right)\mathrm{dt}\:\: \\ $$$$\mathrm{Deduce}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A} \\ $$ Commented…
Question Number 75225 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{xln}\mid\mathrm{x}\mid−\left(\mathrm{x}−\mathrm{m}\right)\mathrm{ln}\mid\mathrm{x}−\mathrm{m}\mid\right)=+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9686 by tawakalitu last updated on 24/Dec/16 Answered by mrW last updated on 24/Dec/16 $$\mathrm{u}=\mathrm{log}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \right) \\ $$$$\frac{\mathrm{du}}{\mathrm{dy}}=\frac{\mathrm{2y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }×\mathrm{log}\:\mathrm{e}…
Question Number 75220 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{consider}\:\mathrm{the}\:\mathrm{function}\: \\ $$$$\mathrm{F}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{x}−\mathrm{lnt}\right)\mathrm{dt}\: \\ $$$$\left.\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:,\:\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{exist} \\ $$$$\left.\mathrm{2}\right)\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{tln}\left(\mathrm{x}−\mathrm{lnt}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{F}\:\in\:\mathrm{C}^{\mathrm{1}} \left(\left[\mathrm{1}:\infty\left[,\left[\mathrm{1}:\infty\left[\right)\:\mathrm{and}\:\mathrm{for}\:\right.\right.\right.\right. \\ $$$$\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:\:\mathrm{F}\left(\mathrm{x}\right)=\mathrm{F}'\left(\mathrm{x}\right)+\mathrm{lnx}…
Question Number 140734 by liberty last updated on 12/May/21 $$\mathrm{Let}\:\mathrm{m},\mathrm{n}\:\mathrm{be}\:\mathrm{given}\:\mathrm{positive}\:\mathrm{integers}. \\ $$$$\mathrm{If}\:\mathrm{x}\:\&\:\mathrm{y}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{x}+\mathrm{y}=\:\mathrm{S}\:,\:\mathrm{S}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{that}\:\mathrm{maximize} \\ $$$$\mathrm{Q}=\mathrm{x}^{\mathrm{m}} \mathrm{y}^{\mathrm{n}} \:. \\ $$ Commented by mr…
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Question Number 140695 by Chhing last updated on 11/May/21 $$\mathrm{Differential}\:\mathrm{system} \\ $$$$\begin{cases}{\mathrm{x}'+\mathrm{x}−\mathrm{y}−\mathrm{z}=\mathrm{ae}^{\mathrm{2t}} }\\{\mathrm{y}'+\mathrm{y}−\mathrm{z}−\mathrm{x}=\mathrm{be}^{\mathrm{2t}} }\\{\mathrm{z}'+\mathrm{z}−\mathrm{x}−\mathrm{y}=\mathrm{ce}^{\mathrm{2t}} }\end{cases} \\ $$$$\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{constants} \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$ Answered by mr W…
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…
Question Number 75080 by ~blr237~ last updated on 07/Dec/19 $$\mathrm{Find}\:\mathrm{out}\: \\ $$$$\mathrm{A}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{1}−\sqrt{\mathrm{sinx}}\right)^{\mathrm{n}} \mathrm{cosxdx} \\ $$ Commented by mathmax by abdo last…