Question Number 198982 by sonukgindia last updated on 26/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198845 by sonukgindia last updated on 25/Oct/23 Answered by som(math1967) last updated on 25/Oct/23 $${I}=\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−\mathrm{1}−{x}\right)^{\mathrm{2}} {dx}}{\mathrm{1}+{e}^{\mathrm{1}−\mathrm{1}−{x}} } \\ $$$$=\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}}…
Question Number 198901 by sonukgindia last updated on 25/Oct/23 Answered by witcher3 last updated on 25/Oct/23 $$\int\frac{\left(\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} }{\mathrm{6sin}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{10cos}^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mathrm{e}^{\mathrm{x}} }\mathrm{dx}=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$=\int\frac{\left(\mathrm{1}−\mathrm{tg}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} }{\mathrm{6tg}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{10e}^{\mathrm{x}} }\mathrm{dx} \\…
Question Number 198862 by sonukgindia last updated on 25/Oct/23 Answered by Frix last updated on 25/Oct/23 $$\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{b}}&{{c}}&{{a}}\\{{c}}&{{a}}&{{b}}\end{vmatrix}=\mathrm{3}{abc}−\left({a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} \right)= \\ $$$$=\left({a}+{b}+{c}\right)\left({ab}+{ac}+{bc}−\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \right)\right)=…
Question Number 198855 by mokys last updated on 25/Oct/23 $${prove}\::\:\underset{{n}\rightarrow\infty} {{lim}}\:\frac{{n}!}{{n}^{{x}} \left({n}−{x}\right)!}\:=\:\mathrm{1}\: \\ $$ Answered by witcher3 last updated on 25/Oct/23 $$\frac{\Gamma\left(\mathrm{n}+\mathrm{1}\right)}{\Gamma\left(\mathrm{n}+\mathrm{1}−\mathrm{x}\right)\mathrm{n}^{\mathrm{x}} } \\ $$$$\Gamma\left(\mathrm{z}\right)=\sqrt{\mathrm{2}\pi}.\mathrm{z}^{\mathrm{z}−\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 198849 by sonukgindia last updated on 25/Oct/23 Commented by mr W last updated on 25/Oct/23 $${for}\:{a},{b},\:{c}\:\in{R}\:{no}\:{solution}! \\ $$ Answered by AST last updated…
Question Number 198806 by sonukgindia last updated on 24/Oct/23 Answered by Frix last updated on 24/Oct/23 $$\int\frac{\mathrm{7}{x}^{\mathrm{2}} +\mathrm{5}}{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{25}}{dx}= \\ $$$$=\int\left(\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}\right)}−\frac{\mathrm{3}{x}−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\right)}\right){dx}= \\…
Question Number 198785 by sonukgindia last updated on 24/Oct/23 Answered by AST last updated on 24/Oct/23 $$\frac{\mathrm{1}}{\mathrm{197}}\equiv{x}\left({mod}\:\mathrm{3000}\right)\Rightarrow\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{3000}\right) \\ $$$$\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{3}\right)\Rightarrow−{x}\overset{\mathrm{3}} {\equiv}\mathrm{1}\Rightarrow{x}\overset{\mathrm{3}} {\equiv}\mathrm{2} \\ $$$$\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{8}\right)\Rightarrow{x}\overset{\mathrm{8}} {\equiv}\mathrm{5} \\…
Question Number 198786 by sonukgindia last updated on 24/Oct/23 Commented by Frix last updated on 24/Oct/23 $$\mathrm{If}\:{a},\:{b},\:{c},\:{d},\:{e}\:\in\mathbb{N}: \\ $$$$\mathrm{1}.\:{abc}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3} \\ $$$$\mathrm{2}.\:{bcd}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{3}.\:{cde}=\mathrm{2}^{\mathrm{3}}…
Question Number 198565 by tri26112004 last updated on 22/Oct/23 $${Let}\:{a},{b},{c}\:\in\:{R}^{+} \:{such}\:{that}\:{a}+{b}+{c}=\mathrm{1}. \\ $$$$\:{Prove}\:{that}:\:\:\:\:{b}+{c}\geqslant\mathrm{16}{abc} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com