Question Number 66304 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left({x}+\mathrm{1}+{sin}\left(\pi{x}\right)\right)}{{xsin}\left(\mathrm{2}{x}\right)} \\ $$ Answered by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({x}+\mathrm{1}+\pi{x}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\:\overset{{hop}}…
Question Number 769 by rishabh last updated on 09/Mar/15 $${Prove}\:{that}\:{product}\:{of}\:{any}\:\:{n}\:{consecutive}\:{integers} \\ $$$${is}\:{divisiblr}\:{by}\:{n}! \\ $$ Commented by 123456 last updated on 09/Mar/15 $${n}\left({n}+\mathrm{1}\right)\centerdot\centerdot\centerdot\left(\mathrm{2}{n}−\mathrm{1}\right) \\ $$ Answered…
Question Number 66302 by ajfour last updated on 12/Aug/19 $${solved}\:{the}\:{general}\:{quintic}, \\ $$$${despite}\:{whatever}\:{proof}\:{that}\:{it} \\ $$$${cant}\:{be}\:{solved}\:{in}\:{a}\:{simple}\:{way}! \\ $$ Commented by mr W last updated on 12/Aug/19 $${i}\:{knew}\:{you}'{ll}\:{tell}\:{us}\:{the}\:{good}\:{news}.…
Question Number 767 by 123456 last updated on 09/Mar/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\frac{{d}\left({fg}\right)}{{dx}}=\frac{{df}}{{dx}}\centerdot\frac{{dg}}{{dx}} \\ $$$$\frac{{d}\left({f}^{\mathrm{2}} \right)}{{dx}}=\frac{{df}}{{dx}}\centerdot\frac{{df}}{{dx}} \\ $$$$\frac{{d}\left({g}^{\mathrm{2}} \right)}{{dx}}=? \\ $$ Commented by 123456…
Question Number 131836 by liberty last updated on 09/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\left(\mathrm{2}+\mathrm{cos}\:\mathrm{x}\right)−\mathrm{3sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} } \\ $$ Commented by EDWIN88 last updated on 10/Feb/21 $$\mathrm{another}\:\mathrm{way}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 765 by prakash jain last updated on 09/Mar/15 $$\mathrm{List}\:\mathrm{all}\:\mathrm{primes}\:{p}\:\mathrm{for}\:\mathrm{which}\:{p}+\mathrm{2}\:\mathrm{and}\:{p}+\mathrm{4} \\ $$$$\mathrm{are}\:\mathrm{also}\:\mathrm{primes}. \\ $$ Answered by rishabh last updated on 09/Mar/15 $${p}=\mathrm{3}\:\mathrm{is}\:\mathrm{the}\:\mathrm{only}\:\mathrm{such}\:\mathrm{number}. \\ $$$$\mathrm{Let}\:\mathrm{us}\:\mathrm{assume}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:{p}>\mathrm{3}.…
Question Number 764 by prakash jain last updated on 13/Mar/15 $$\mathrm{tan}\:{x}+\mathrm{tan}\:\mathrm{2}{x}+\mathrm{tan}\:\mathrm{4}{x}+…+\mathrm{tan}\:\mathrm{2}^{{n}} {x}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131828 by Salman_Abir last updated on 09/Feb/21 Answered by liberty last updated on 09/Feb/21 $$\mathrm{20}\:=\:\frac{\mathrm{6}!}{\mathrm{3}!.\mathrm{3}!} \\ $$ Commented by Salman_Abir last updated on…
Question Number 758 by 13/NaSaNa(N)056565 last updated on 08/Mar/15 $$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$ Commented by malwaan last updated on 08/Mar/15 $${integral}\:{by}\:{parts} \\ $$$$\int{udv}={uv}−\int{vdu}\:…
Question Number 757 by 123456 last updated on 07/Mar/15 $${k}\frac{{d}^{\mathrm{2}} {i}}{{dt}^{\mathrm{2}} }+{l}\frac{{di}}{{dt}}+{ri}={v} \\ $$$${i}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${i}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${k},{l},{r},{v}\:{are}\:{constants} \\ $$ Commented by prakash jain last…