Question Number 67513 by mhmd last updated on 28/Aug/19 $$\int{x}^{{n}\:} {lnx}/{n}^{{x}} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1976 by 123456 last updated on 27/Oct/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){g}\left({x}\right)+{f}\left({y}\right){g}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{g}\left({x}\right){g}\left({y}\right) \\ $$$$\left[{f}\left({x}\right)\right]^{\mathrm{2}} +\left[{g}\left({x}\right)\right]^{\mathrm{2}} =? \\ $$$$\left[{f}\left({x}\right)+{g}\left({y}\right)\right]\left[{g}\left({x}\right)+{f}\left({y}\right)\right]=?? \\ $$$${f}\left({x}\right)=??? \\…
Question Number 1970 by 123456 last updated on 27/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${xf}\left({x}\right)={f}\left[{f}\left({x}\right)\right]{f}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 27/Oct/15 $${f}\left({x}\right)\neq\mathrm{0}\:\mathrm{then}\:{f}\left({f}\left({x}\right)={x}\right.…
Question Number 133036 by liberty last updated on 18/Feb/21 $$\underset{\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2014}} \left({x}\right)}\:=\:\frac{\pi\mathrm{e}^{\mathrm{q}} }{\mathrm{p}} \\ $$$$\mathrm{Find}\:\mathrm{2p}−\mathrm{q}.\: \\ $$ Answered by liberty last updated on 18/Feb/21…
Question Number 133038 by liberty last updated on 18/Feb/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:=? \\ $$ Commented by Dwaipayan Shikari last updated on 18/Feb/21…
Question Number 67501 by TawaTawa last updated on 28/Aug/19 $$\mathrm{Show}\:\mathrm{that}\:\:\mathrm{1n}^{\mathrm{3}} \:+\:\mathrm{2n}\:+\:\mathrm{3n}^{\mathrm{2}} \:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2}\:\mathrm{and}\:\mathrm{3}\:\mathrm{for}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{n}. \\ $$ Commented by Prithwish sen last updated on 28/Aug/19 $$\mathrm{Another}\:\mathrm{approch} \\ $$$$\mathrm{We}\:\mathrm{know}\:\mathrm{that}…
Question Number 1964 by 123456 last updated on 26/Oct/15 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{{cy}}{{x}^{\mathrm{2}} } \\ $$$${y}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 26/Oct/15…
Question Number 1963 by 123456 last updated on 26/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R},{a}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${a}_{{n}+\mathrm{1}} ={f}\left({a}_{{n}} \right)−{a}_{{n}} \\ $$$${f}\left({x}\right)\geqslant{f}\left({y}\right),\forall{x}\geqslant{y}\geqslant\mathrm{0} \\ $$$$\mathrm{does} \\ $$$${a}_{{n}} \geqslant{a}_{{m}} ,\forall{n}\geqslant{m}\geqslant\mathrm{0}? \\ $$ Answered…
Question Number 1961 by alib last updated on 26/Oct/15 $${Solve}… \\ $$$$ \\ $$$$\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:=\:{sin}\:{x}\:+\:{cos}\:{x} \\ $$ Answered by Rasheed Soomro last updated on 26/Oct/15 $$\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:=\:{sin}\:{x}\:+\:{cos}\:{x}…
Question Number 133028 by mohammad17 last updated on 18/Feb/21 Answered by Dwaipayan Shikari last updated on 18/Feb/21 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{1},\mathrm{1}\right)} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}−{y}}={x}+{y}=\mathrm{2} \\ $$ Terms of…