Question Number 151685 by iloveisrael last updated on 22/Aug/21 $$\:\:{Find}\:{maximum}\:{value}\:{of}\:{function} \\ $$$$\:\:\alpha\left({x}\right)=\:\sqrt{\mathrm{2}{x}}\:+\sqrt{\mathrm{16}−{x}}\:+\sqrt{\mathrm{35}+{x}}\:. \\ $$ Answered by mr W last updated on 22/Aug/21 $${x}\geqslant\mathrm{0} \\ $$$${x}\leqslant\mathrm{16}…
Question Number 86092 by ar247 last updated on 27/Mar/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by abdomathmax last updated on 27/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{\:\sqrt{−\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}}}\:\:{we}\:{have} \\ $$$${I}=\int\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}−\mathrm{1}\right)}}=\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 20205 by vivek last updated on 24/Aug/17 $${find}\:{the}\:{sin}^{−\mathrm{1}} \:{diferentiation} \\ $$ Answered by Joel577 last updated on 24/Aug/17 $${y}\:=\:\mathrm{sin}^{−\mathrm{1}} \:\left({x}\right) \\ $$$${x}\:=\:\mathrm{sin}\:{y} \\…
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Question Number 151118 by mnjuly1970 last updated on 18/Aug/21 $$\:\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{arctan}\left(\frac{{x}}{\mathrm{2}}\right)+{arctan}\left(\mathrm{2}{x}\right)}{{x}^{\:\mathrm{2}} +\mathrm{1}}\overset{?} {=}\frac{\pi^{\:\mathrm{2}} }{\mathrm{4}} \\ $$$$ \\ $$ Answered by Olaf_Thorendsen last…
Question Number 151114 by mnjuly1970 last updated on 18/Aug/21 $$ \\ $$$$\:\:\:\:\:{solve}…. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Q}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\:\left({x}\:\right).\:{ln}\:\left(\:\mathrm{2}−\:{x}\:\right){dx}\:=?\:………..\blacksquare \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970}… \\ $$$$ \\…
Question Number 85513 by niroj last updated on 22/Mar/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{cot}}\:\boldsymbol{\mathrm{x}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:=\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \\ $$ Answered by mr W last updated on 22/Mar/20 $$\frac{{dy}}{{dx}}=−{y}\:\mathrm{cot}\:{x}\pm\sqrt{{y}^{\mathrm{2}} \mathrm{cot}^{\mathrm{2}}…
Question Number 19903 by j.masanja06@gmail.com last updated on 17/Aug/17 $$\mathrm{by}\:\mathrm{use}\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{principle},\mathrm{find} \\ $$$$\mathrm{dy}/\mathrm{dx}\:\mathrm{of}\: \\ $$$$\mathrm{y}=\mathrm{cos}\left(\mathrm{x}−\frac{\Pi}{\mathrm{8}}\right) \\ $$ Answered by icyfalcon999 last updated on 18/Aug/17…
Question Number 150963 by EDWIN88 last updated on 17/Aug/21 $${Given}\:{x}\:,{y}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:\mathrm{0}<\frac{{y}}{{x}}<\frac{\mathrm{1}}{\mathrm{2}}.\:{Find}\:{minimum}\:{value} \\ $$$${of}\:\frac{\mathrm{2}{y}}{{x}−{y}}\:+\frac{\mathrm{3}{x}}{{x}+\mathrm{2}{y}}\:.\: \\ $$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{let}\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{t}\:\Rightarrow\mathrm{f}\left(\mathrm{t}\right)=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}}+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{2t}}\: \\…