Question Number 126039 by snipers237 last updated on 16/Dec/20 $${Let}\:{A}=\left[\mathrm{2};\infty\left[^{\mathrm{2}} \:\:{and}\:{f}\:\in\left(\mathbb{R}×\mathbb{R}\right)^{\mathbb{R}} \:{such}\:{as}\:\right.\right. \\ $$$${f}\left({x},{y}\right)=\frac{\chi_{{A}} \left({x},{y}\right)}{{E}\left({x}\right)^{{E}\left({y}\right)} }\:\:{where}\:\chi_{{A}} \:{is}\:{the}\:{caracteristic}\:{function}\:{of}\:{A} \\ $$$$\:{Prove}\:{that}\:{f}\:{is}\:{a}\:{density}\:{of}\:{a}\:{probability}\:{P} \\ $$ Answered by mindispower last…
Question Number 126010 by bramlexs22 last updated on 16/Dec/20 Answered by liberty last updated on 16/Dec/20 $${The}\:{area}\:{of}\:{a}\:{tringle}\:{is}\:{A}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{8}\right)\left(\mathrm{6}\right)\mathrm{sin}\:\theta \\ $$$${A}\:=\:\mathrm{24}\:\mathrm{sin}\:\theta \\ $$$$\frac{{dA}}{{dt}}\:=\:\left(\mathrm{24}\:\mathrm{cos}\:\theta\right)\:\frac{{d}\theta}{{dt}}\:;\:{where}\:\frac{{d}\theta}{{dt}}\:=\:\mathrm{0}.\mathrm{12}\:{rad}/{sec} \\ $$$$\Leftrightarrow\:\frac{{dA}}{{dt}}\:=\:\mathrm{24}×\mathrm{0}.\mathrm{12}×\mathrm{cos}\:\frac{\pi}{\mathrm{6}}=\:\mathrm{2}.\mathrm{49}\:{m}^{\mathrm{2}} /{sec}\: \\…
Question Number 126008 by bramlexs22 last updated on 16/Dec/20 $$\:{Find}\:{all}\:{asymptotes}\:{of}\:{the}\: \\ $$$${function}\:{y}=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:. \\ $$ Answered by liberty last updated on 16/Dec/20 $${Horizontal}\:{asymptote}\::\:{y}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:=\:\underset{{x}\rightarrow\infty}…
Question Number 126003 by mnjuly1970 last updated on 16/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{integral}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {tan}\left({x}\right){ln}\left({sin}\left({x}\right)\right){ln}\left({cos}\left({x}\right)\right){dx}=\frac{\zeta\left(\mathrm{3}\right.}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{G}{ood}\:{luck} \\ $$ Answered by Olaf last updated…
Question Number 125996 by bramlexs22 last updated on 16/Dec/20 $$\:{If}\:{z}^{\mathrm{3}} ={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:,\:\rightarrow\begin{cases}{\frac{{dx}}{{dt}}=\mathrm{3}}\\{\frac{{dy}}{{dt}}=\mathrm{2}}\end{cases} \\ $$$${find}\:\frac{{dz}}{{dt}}\:{when}\:{x}=\mathrm{4}\:{and}\:{y}=\mathrm{1} \\ $$ Answered by Olaf last updated on 16/Dec/20 $${z}^{\mathrm{3}}…
Question Number 125995 by liberty last updated on 16/Dec/20 Commented by benjo_mathlover last updated on 16/Dec/20 $${f}\left({x}\right)=\:\begin{cases}{{x}\:;\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{−{x}\:;\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{0}}\end{cases} \\ $$$$\:{f}\:'\left(−\mathrm{1}\right)\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left(−\mathrm{1}+{h}\right)−{f}\left(−\mathrm{1}\right)}{{h}} \\ $$$${f}\:'\left(−\mathrm{1}\right)=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\left(−\mathrm{1}+{h}\right)−\left(\mathrm{1}\right)}{{h}} \\ $$$$\:{f}\:'\left(−\mathrm{1}\right)=\:\underset{{h}\rightarrow\mathrm{0}}…
Question Number 191528 by mnjuly1970 last updated on 25/Apr/23 $$ \\ $$$$\:\:\:\:\:\:{find}\:\:{the}\:\:{value}\:\:{of}\:\:{the} \\ $$$$\:\:\:\:\:\:\:{following}\:\:{series}\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\frac{{n}\pi}{\mathrm{4}}\:\right)}{{n}^{\:\mathrm{2}} }\:=? \\ $$ Answered by…
Question Number 60426 by cesar.marval.larez@gmail.com last updated on 20/May/19 $${the}\:{function}\:{is}\:{considered}\: \\ $$$${f}\left({x},{y}\right)={e}^{{xy}} +\frac{{x}}{{y}}+{sen}\left(\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\pi\right)\:{Calcule}: \\ $$$$\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} },\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}.\:\:\:{f}_{{x}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{y}} \left(\mathrm{2},−\mathrm{1}\right),\:{f}_{{xx}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{xy}} \left(\mathrm{2},−\mathrm{1}\right) \\ $$ Commented…
Question Number 60425 by cesar.marval.larez@gmail.com last updated on 20/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125925 by zarminaawan last updated on 15/Dec/20 $$\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }−\mathrm{2}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{4}\frac{{dy}}{{dx}}−\mathrm{8}{y}=\mathrm{0} \\ $$ Answered by liberty last updated on 15/Dec/20 $${HE}\:\equiv\:{z}^{\mathrm{3}} −\mathrm{2}{z}^{\mathrm{2}}…