Question Number 143790 by Dwaipayan Shikari last updated on 18/Jun/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{3}} }{{n}^{\mathrm{3}} }\right) \\ $$ Commented by Dwaipayan Shikari last updated on 18/Jun/21…
Question Number 78251 by aliesam last updated on 15/Jan/20 $$\int\frac{{x}+\mathrm{4}}{{x}−\sqrt[{\mathrm{3}}]{{x}}}\:{dx}\: \\ $$ Answered by john santu last updated on 15/Jan/20 $${let}\:{x}\:=\:{u}^{\mathrm{3}} \:\Rightarrow{dx}=\mathrm{3}{u}^{\mathrm{2}} \:{du} \\ $$$$\int\:\frac{{u}^{\mathrm{3}}…
Question Number 12714 by ashok kumar last updated on 29/Apr/17 Commented by ashok kumar last updated on 29/Apr/17 $$\boldsymbol{\mathrm{W}{hat}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{\theta}. \\ $$ Terms of Service Privacy…
Question Number 12713 by ashok kumar last updated on 29/Apr/17 $$\boldsymbol{{Q}}.\:\boldsymbol{\theta}\:=\:\mathrm{tan}^{−\mathrm{1}} \:\:\mathrm{4}/\mathrm{3}\: \\ $$$$ \\ $$ Commented by prakash jain last updated on 01/May/17 $$\mathrm{agar}\:\mathrm{ye}\:\mathrm{textbook}\:\mathrm{ka}\:\mathrm{question}\:\mathrm{hai}…
Question Number 143786 by mohammad17 last updated on 18/Jun/21 $$\int_{−\infty} ^{\:\infty} \frac{{e}^{{iax}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:\:\:\:\:{how}\:{can}\:{it}\:{solve}\:{this} \\ $$ Commented by mohammad17 last updated on 18/Jun/21 $$????? \\…
Question Number 143781 by bemath last updated on 18/Jun/21 Answered by liberty last updated on 18/Jun/21 $$\mathrm{let}\:\mathrm{x}+\mathrm{1}=\:\mathrm{t}\Rightarrow\mathrm{f}\left(\mathrm{t}−\mathrm{1}\right)=\mathrm{y}=\frac{\left(\mathrm{t}+\mathrm{9}\right)\left(\mathrm{t}+\mathrm{1}\right)}{\mathrm{t}} \\ $$$$\mathrm{y}=\mathrm{t}+\mathrm{10}+\frac{\mathrm{9}}{\mathrm{t}}\:.\Rightarrow\:\mathrm{t}+\frac{\mathrm{9}}{\mathrm{t}}\:\mathrm{has}\:\mathrm{minimum}\:\mathrm{6}\:\mathrm{for}\:\mathrm{t}=\mathrm{3}\: \\ $$$$\mathrm{so}\:\mathrm{f}\left(\mathrm{t}\right)_{\mathrm{min}} =\mathrm{3}+\mathrm{10}+\frac{\mathrm{9}}{\mathrm{3}}=\mathrm{16} \\ $$ Answered…
Question Number 78246 by MJS last updated on 15/Jan/20 $$\mathrm{common}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{conic}\:\mathrm{sections} \\ $$$${ax}^{\mathrm{2}} +{bxy}+{cy}^{\mathrm{2}} +{dx}+{ey}+{f}=\mathrm{0} \\ $$$$\mathrm{if}\:{b}\neq\mathrm{0}\:\mathrm{we}\:\mathrm{rotate} \\ $$$$\mathrm{tan}\:\mathrm{2}\alpha\:=\frac{{b}}{{a}−{c}}\:\left[\mathrm{if}\:{a}={c}\:\Rightarrow\:\alpha=\mathrm{45}°\right] \\ $$$$\begin{cases}{{x}={x}'\mathrm{cos}\:\alpha\:−{y}'\mathrm{sin}\:\alpha}\\{{y}={x}'\mathrm{sin}\:\alpha\:+{y}'\mathrm{cos}\:\alpha}\end{cases} \\ $$$$\mathrm{we}\:\mathrm{now}\:\mathrm{have}\:\left[\mathrm{using}\:{x},\:{y}\:\mathrm{again}\:\mathrm{instead}\:\mathrm{of}\:{x}',\:{y}'\right] \\ $$$${Ax}^{\mathrm{2}} +{Cy}^{\mathrm{2}}…
Question Number 143783 by mnjuly1970 last updated on 18/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\Omega\::=\int_{−\infty} ^{\:\infty} \frac{{log}\left(\mathrm{2}+{x}^{\:\mathrm{2}} \right)}{\mathrm{4}+{x}^{\:\mathrm{2}} }{dx}=? \\ $$$$ \\ $$ Answered by mindispower last updated…
Question Number 12708 by @ANTARES_VY last updated on 29/Apr/17 $$\boldsymbol{\mathrm{what}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{values}}\:\:\boldsymbol{\alpha}. \\ $$$$\boldsymbol{\mathrm{y}}=\mathrm{2}\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} −\boldsymbol{\alpha\mathrm{e}}^{−\boldsymbol{\mathrm{x}}} +\left(\mathrm{2}\boldsymbol{\alpha}+\mathrm{1}\right)\boldsymbol{\mathrm{x}}−\mathrm{3} \\ $$$$\boldsymbol{\mathrm{will}}\:\:\boldsymbol{\mathrm{feature}}\:\:\boldsymbol{\mathrm{all}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{outlets}} \\ $$$$\boldsymbol{\mathrm{growing}}. \\ $$ Terms of Service Privacy Policy…
Question Number 143776 by akmalovna05 last updated on 18/Jun/21 $$\mathrm{x}×\mathrm{y}''−\mathrm{y}=\mathrm{x}^{\mathrm{3}} \\ $$ Answered by Olaf_Thorendsen last updated on 18/Jun/21 $${xy}''−{y}\:=\:{x}^{\mathrm{3}} \:\:\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Particular}\:\mathrm{solution}\::…