Question Number 131684 by aurpeyz last updated on 07/Feb/21 Answered by ajfour last updated on 07/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\circleddash\left(−\mathrm{2}\mu{C}\:\right)\:\:\:\:\:\:\:\:\:\:\:\oplus\left(\mathrm{10}\mu{C}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{4}\pi\epsilon_{\mathrm{0}} }\frac{\mid{q}_{\mathrm{3}} {q}_{\mathrm{2}} \mid}{{r}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{4}\pi\epsilon_{\mathrm{0}} }\frac{\mid{q}_{\mathrm{3}} {q}_{\mathrm{1}}…
Question Number 613 by 123456 last updated on 11/Feb/15 $$\Xi\left({a},{b},{c},{d}\right)=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}^{{a}} \left(\pi{x}\right)\mathrm{cos}^{{b}} \left(\pi{x}\right)}{{x}^{{c}} \left(\mathrm{1}−{x}\right)^{{d}} }{dx} \\ $$$$\Xi\left(\mathrm{1},\mathrm{1},\mathrm{1},\mathrm{1}\right)=? \\ $$ Commented by prakash jain last…
Question Number 131686 by Dwaipayan Shikari last updated on 07/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\pi\right)}{{n}^{\mathrm{3}} } \\ $$ Commented by Dwaipayan Shikari last updated on 07/Feb/21 $${I}\:{have}\:{found}\:\frac{\mathrm{7}\pi^{\mathrm{3}}…
Question Number 66149 by Rio Michael last updated on 09/Aug/19 $${f}\left({x}\right)\:=\mathrm{2}{x}^{\mathrm{3}} −{x}−\mathrm{4}\: \\ $$$${show}\:{that}\:{f}\left({x}\right)\:=\mathrm{0}\:{has}\:{roots}\:{between} \\ $$$$\mathrm{1}\:{and}\:\mathrm{2} \\ $$ Answered by MJS last updated on 09/Aug/19…
Question Number 612 by 123456 last updated on 08/Mar/15 $${encontre}\:{f}:\mathbb{N}\rightarrow\mathbb{N}\:{sobrejetivo}\:{tal}\:{que} \\ $$$${f}^{−\mathrm{1}} \left({n}\right)=\left\{{m}\mid{f}\left({m}\right)={n}\right\}\:{e}\:{infinito} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66140 by AnjanDey last updated on 09/Aug/19 $$\mathrm{1}.\boldsymbol{{Show}}\:\boldsymbol{{that}}:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\:\mathrm{2}{x}\right)\mathrm{sin}\:{x}\:{dx}=\sqrt{\mathrm{2}}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {f}\left(\mathrm{cos}\:\mathrm{2}{x}\right)\mathrm{cos}\:{x}\:{dx}. \\ $$$$\mathrm{2}.\boldsymbol{{If}}\:\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)=\frac{\boldsymbol{{d}}}{\boldsymbol{{dz}}}\left\{\mathrm{5}^{\mid\boldsymbol{{f}}\left(\boldsymbol{{z}}\right)\mid} \right\}\:\:\boldsymbol{{then}}\:\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{f}}'\left(\boldsymbol{{e}}\right)? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 605 by magmarsenpai last updated on 10/Feb/15 $${Given}\:{a}\:{matrix}\:{A}\:\in\:\mathbb{M}_{{n}\:×\:{n}\:} \:\forall\:\:{k}\:\in\:\mathbb{N}\:{define}: \\ $$$${A}=\begin{cases}{\varnothing_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:{A}=\varnothing\:\:{and}\:\:{k}\geqslant\mathrm{1}}\\{{I}_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:{A}\neq\varnothing_{{n}} \:{and}\:{k}\neq\mathrm{0}}\\{{A}^{{k}−\mathrm{1}} {A}\:\:\:\:{if}\:{A}\neq\varnothing_{{n}} \:{and}\:{k}\geqslant\mathrm{1}}\end{cases} \\ $$$${Prove}\:{that}\:{A}^{{k}} {A}^{{r}} ={A}^{{k}+{r}} \:\forall\:{k},{r}\:\in\:\mathbb{N}. \\ $$…
Question Number 131678 by liberty last updated on 07/Feb/21 $$\:\mathrm{Nice}\:\mathrm{calculus}\: \\ $$$$\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{n}−\mathrm{2}} \:−\mathrm{1}}{\mathrm{x}^{\mathrm{n}} \:+\mathrm{1}}\:\mathrm{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 604 by 123456 last updated on 09/Feb/15 $$\underset{\mathrm{0}} {\overset{+\mathrm{1}} {\int}}\left(\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\frac{\mathrm{1}−{x}^{\mathrm{4}} {y}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{2}} {y}}{dx}\right){dy} \\ $$ Answered by prakash jain last updated…
Question Number 131673 by liberty last updated on 07/Feb/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\mathrm{x}\right)}{\mathrm{ln}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by mindispower last updated on 07/Feb/21 $${ln}\left({x}\right)=−{t} \\…