Question Number 153212 by mnjuly1970 last updated on 05/Sep/21 $$ \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \frac{\:{tan}\left({x}\right).{Arctanh}\left({cos}\left({x}\right)\right)}{{x}}{dx}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153189 by liberty last updated on 05/Sep/21 Answered by EDWIN88 last updated on 05/Sep/21 $$\:{eq}\:{of}\:{circle}\:\mathrm{16}{x}^{\mathrm{2}} +\mathrm{16}{y}^{\mathrm{2}} +\mathrm{48}{x}−\mathrm{8}{y}−\mathrm{43}= \\ $$$${with}\:{center}\:{point}\:\begin{cases}{{x}=−\frac{\mathrm{48}}{\mathrm{32}}=−\frac{\mathrm{3}}{\mathrm{2}}}\\{{y}=\frac{\mathrm{8}}{\mathrm{32}}=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$${with}\:{radius}\:=\sqrt{\frac{\mathrm{9}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}−\left(\frac{−\mathrm{43}}{\mathrm{16}}\right)} \\ $$$$\Rightarrow{r}=\sqrt{\frac{\mathrm{36}+\mathrm{1}+\mathrm{43}}{\mathrm{16}}}\:=\frac{\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{4}}=\sqrt{\mathrm{5}}\:…
Question Number 22105 by j.masanja06@gmail.com last updated on 11/Oct/17 $${use}\:{the}\:{first}\:{principle}\:{to}\:{find} \\ $$$${value}\:{of} \\ $$$${f}\left({x}\right)=\left({x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Answered by $@ty@m last updated on 11/Oct/17 $$\frac{{dy}}{{dx}}=\underset{\delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({x}+\delta{x}\right)−{f}\left({x}\right)}{\delta{x}}…
Question Number 87532 by niroj last updated on 04/Apr/20 $$\:\left(\mathrm{1}\right).\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{general}}\:\boldsymbol{\mathrm{solution}}: \\ $$$$\:\:\:\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{px}}\:+\boldsymbol{\mathrm{p}}^{\boldsymbol{\mathrm{n}}} \\ $$$$\:\left(\mathrm{2}\right).\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:+\:\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\:\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{4}\right). \\ $$$$\:\: \\ $$ Commented by…
Question Number 21964 by chernoaguero@gmail.com last updated on 07/Oct/17 Answered by ibraheem160 last updated on 07/Oct/17 $$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \left(\mathrm{2x}−\mathrm{5}\right)^{\mathrm{4}} \\ $$$$\frac{\mathrm{du}}{\mathrm{dx}}=\mathrm{2x},\:\:\frac{\mathrm{dv}}{\mathrm{dx}}=\mathrm{8}\left(\mathrm{2x}−\mathrm{5}\right)^{\mathrm{3}} \\ $$$$\: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{u}\frac{\mathrm{dv}}{\mathrm{dx}}+\mathrm{v}\frac{\mathrm{du}}{\mathrm{dx}} \\…
Question Number 152947 by mnjuly1970 last updated on 03/Sep/21 $$ \\ $$$$\:\:\:{prove}\::: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:\infty} \:\frac{\:{e}^{\:−\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }} }{{x}^{\:\mathrm{4}} }\:{dx}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\Gamma\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right) \\ $$$$ \\ $$ Answered…
Question Number 87378 by jagoll last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{3x}−\mathrm{3tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$ Commented by john santu last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{3x}+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{3x}\right)^{\mathrm{3}} +\mathrm{o}\left(\left(\mathrm{3x}\right)^{\mathrm{3}}…
Question Number 152904 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{1}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\mathrm{x}+\mathrm{5sin}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:=−\mathrm{4}\:\mathrm{sin}\:\mathrm{x}+\mathrm{5}\:\mathrm{cos}\:× \\ $$$$\left.\mathrm{2}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\:\mathrm{sin}\:\mathrm{2x}\:−\:\mathrm{5}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\mathrm{3}×\mathrm{2}\:\mathrm{cos}\:\mathrm{2x}\:+\mathrm{5}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{6}\:\mathrm{cos}\:\mathrm{2x}\:+\:\mathrm{5}\:\mathrm{sin}\:\mathrm{x}//…
Question Number 152797 by mnjuly1970 last updated on 01/Sep/21 $$ \\ $$$$\:\:\:{nice}..{mathematics}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}… \\ $$$$\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{cos}\:\left({x}\:\right)}{{cosh}\:\left({x}\:\right)}\:{dx}=\frac{\pi}{\:{cosh}\:\left(\frac{\pi}{\mathrm{2}}\:\right)}\:…….\blacksquare\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:{prepared}\:::\:\:{m}.{n} \\ $$$$ \\…
Question Number 152795 by mnjuly1970 last updated on 01/Sep/21 $$ \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\:\right)}{{x}}\left(\frac{{a}^{\:\mathrm{2}} +{cos}^{\:\mathrm{2}} \left({x}\right)}{{b}^{\:\mathrm{2}} +\:{cos}^{\:\mathrm{2}} \left({x}\:\right)}\right){dx}=? \\ $$$$ \\ $$ Answered by Olaf_Thorendsen…