Question Number 12591 by @ANTARES_VY last updated on 26/Apr/17 $$\boldsymbol{\mathrm{This}} \\ $$$$\oint\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sphere}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{values}} \\ $$ Commented by ajfour last updated on…
Question Number 12580 by @ANTARES_VY last updated on 26/Apr/17 $$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{smaillest}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right). \\ $$ Answered by ajfour last updated on 26/Apr/17 $$\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\left({x}^{\mathrm{2}}…
Question Number 12562 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{y}}=−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{3}}+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{maximum}}−\boldsymbol{\mathrm{minimum}}=? \\ $$ Commented by sandy_suhendra last updated on 25/Apr/17 $$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:''\mathrm{max}\:\mathrm{stationary}''\:\mathrm{and}\:''\mathrm{min}\:\mathrm{stationary}''\:? \\…
Question Number 12558 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{This}}\:\: \\ $$$$\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{12}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{values}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{area}}. \\ $$ Answered by ajfour last updated on 25/Apr/17 $${y}=−\mathrm{12}−\left[\left({x}−\mathrm{3}\right)^{\mathrm{2}}…
Question Number 12551 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{This}}\:\:\boldsymbol{\mathrm{y}}=\frac{\mathrm{2}\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{smallest}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$ Answered by mrW1 last updated on 25/Apr/17 $$\boldsymbol{\mathrm{y}}=\frac{\mathrm{2}\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{sin}}^{\mathrm{2}}…
Question Number 12552 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{expression}}. \\ $$$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{8}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}.} \\ $$ Answered by ajfour last updated on 25/Apr/17 $${if}\:{you}\:{mean}\:{the}\:{range}\:{then} \\…
Question Number 12547 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{This}} \\ $$$$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{sin}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{range}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\: \\ $$$$\boldsymbol{\mathrm{function}}. \\ $$ Answered by mrW1 last updated on 25/Apr/17 $${x},{y}\in\mathbb{R} \\…
Question Number 12543 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{This}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\alpha\mathrm{x}}+\boldsymbol{\alpha}−\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{1}} \:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{a}}\:\:\boldsymbol{\mathrm{what}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{1}} ^{\mathrm{2}} +\boldsymbol{\mathrm{x}}_{\mathrm{2}} ^{\mathrm{2}} \:\:\boldsymbol{\mathrm{this}}\:\:\boldsymbol{\mathrm{collection}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{smille}}\left(\boldsymbol{\mathrm{minimum}}\right)\:\:\boldsymbol{\mathrm{value}}. \\…
Question Number 143609 by mnjuly1970 last updated on 16/Jun/21 $$\:\:\: \\ $$$$\:{Prove}\:{that}:: \\ $$$$\:\:\Omega:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right).{ln}\left({x}\right)}{{x}}{dx}=\frac{−\mathrm{1}}{\mathrm{2}}\:\zeta\:\left(\mathrm{4}\:\right) \\ $$$${Without}\:{using}\:{the}\:“{Beta}\:{function}'' \\ $$$$\:\:{m}.{n} \\ $$ Answered by…
Question Number 78046 by jagoll last updated on 13/Jan/20 $${minimum}\:{of}\: \\ $$$${function}\:{y}\:=\:\sqrt{{x}^{\mathrm{2}} +{e}^{\mathrm{2}{x}} }\:\:{is} \\ $$ Answered by john santu last updated on 13/Jan/20 $${y}'\:=\:\frac{\mathrm{2}{x}+\mathrm{2}{e}^{\mathrm{2}{x}}…