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 $${if}\:{you}\:{mean}\:{the}\:{range}\:{then} \\…
Question Number 12551 by @ANTARES_VY last updated on 25/Apr/17 $$\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 $$\boldsymbol{\mathrm{y}}=\frac{\mathrm{2}\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{sin}}^{\mathrm{2}}…
Question Number 143622 by ArielVyny last updated on 16/Jun/21 $$\int_{\mathrm{0}} ^{\propto} {e}^{\mathrm{2}{arctg}\left({t}^{\mathrm{2}} \right)} {dt} \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{arctan}\left({t}\right)\underset{{t}\rightarrow+\infty} {\rightarrow}\frac{\pi}{\mathrm{2}}>\mathrm{0}…
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 $${x},{y}\in\mathbb{R} \\…
Question Number 78083 by TawaTawa last updated on 14/Jan/20 Commented by john santu last updated on 14/Jan/20 $${sir}\:{this}\:{ambigue}\:\mathrm{21600}!\: \\ $$ Commented by TawaTawa last updated…
Question Number 12543 by @ANTARES_VY last updated on 25/Apr/17 $$\boldsymbol{\mathrm{This}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\alpha\mathrm{x}}+\boldsymbol{\alpha}−\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{1}} \:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{a}}\:\:\boldsymbol{\mathrm{what}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{x}}_{\mathrm{1}} ^{\mathrm{2}} +\boldsymbol{\mathrm{x}}_{\mathrm{2}} ^{\mathrm{2}} \:\:\boldsymbol{\mathrm{this}}\:\:\boldsymbol{\mathrm{collection}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{smille}}\left(\boldsymbol{\mathrm{minimum}}\right)\:\:\boldsymbol{\mathrm{value}}. \\…
Question Number 12540 by Mr Chheang Chantria last updated on 25/Apr/17 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\sqrt{\boldsymbol{{x}}}=\sqrt{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143609 by mnjuly1970 last updated on 16/Jun/21 $$\:\:\: \\ $$$$\:{Prove}\:{that}:: \\ $$$$\:\:\Omega:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right).{ln}\left({x}\right)}{{x}}{dx}=\frac{−\mathrm{1}}{\mathrm{2}}\:\zeta\:\left(\mathrm{4}\:\right) \\ $$$${Without}\:{using}\:{the}\:“{Beta}\:{function}'' \\ $$$$\:\:{m}.{n} \\ $$ Answered by…
Question Number 78074 by Rio Michael last updated on 14/Jan/20 $${evaluate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \mathrm{sinh}\:^{−\mathrm{1}} {x}\:{dx}\:\:{and}\:\underset{\mathrm{1}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}\mathrm{tanh}\:^{−\mathrm{1}} {x}\:{dx} \\ $$ Answered by mr W last updated…
Question Number 78075 by Rio Michael last updated on 14/Jan/20 $${expressing}\:\:{P}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} \:+\:{x}}{\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\:{in}\:{partial}\:{fractions}\:{gives} \\ $$$${A}.\:\:\frac{{A}}{\left({x}−\mathrm{3}\right)}\:+\:\frac{{Bx}\:+\:{C}}{\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\: \\ $$$${B}.\:\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\mathrm{2}}\:+\:\frac{{C}}{{x}+\mathrm{2}} \\ $$$${C}.\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\sqrt{\mathrm{2}}}\:+\:\frac{{C}}{{x}\:+\:\sqrt{\mathrm{2}}} \\ $$$${D}.\:\frac{{Ax}\:+\:{B}}{{x}−\mathrm{3}}\:+\:\frac{{C}}{{x}^{\mathrm{2}} −\mathrm{2}} \\ $$…