Question Number 926 by 123456 last updated on 26/Apr/15 $${a}\left({n},{m}\right)=\begin{cases}{{m}}&{{n}\leqslant\mathrm{0}}\\{{na}\left({n}+{m}−\mathrm{1},{m}\right)+{m}}&{{n}>\mathrm{0}\vee{m}\leqslant\mathrm{0}}\\{{na}\left({n}−{m},{m}−\mathrm{1}\right)+{m}+{m}^{\mathrm{2}} }&{{n}>\mathrm{0}\vee{m}>\mathrm{0}}\end{cases} \\ $$$${a}\left(\mathrm{5},\mathrm{5}\right)=??? \\ $$$${a}\left(\mathrm{10},\mathrm{10}\right)=?? \\ $$ Commented by 123456 last updated on 27/Apr/15 $${a}\left(\mathrm{0},{m}\right)={m}…
Question Number 66462 by mathmax by abdo last updated on 15/Aug/19 $$\left.\mathrm{1}\right){simplify}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}} \left({x}\right){cos}\left({kx}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}}…
Question Number 874 by 123456 last updated on 08/Apr/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)={g}\left({x}\right)−{f}\left(−{x}\right) \\ $$$${g}\left({x}\right)={f}\left({x}\right)+{g}\left(−{x}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$$${f}\left({x}\right)+{g}\left({x}\right)=? \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\overset{?} {=}\boldsymbol{{f}}\left(−\boldsymbol{{x}}\right)…
Question Number 863 by 123456 last updated on 30/Mar/15 $${f}\left({xy}\right)={f}\left[{xf}\left({y}\right)\right] \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 30/Mar/15 $${f}\left({y}\right)={y} \\ $$…
Question Number 830 by prakash jain last updated on 20/Mar/15 $${f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}^{\mathrm{2}} \right)={f}\left({x}\right){f}\left({x}−\mathrm{1}\right) \\ $$$$\mathrm{Find}\:{f}\left({x}\right)\:\mathrm{such}\:\mathrm{that}\:{f}\left({x}\right)\neq\mathrm{0}. \\ $$ Commented by 123456 last updated on 23/Mar/15…
Question Number 821 by 123456 last updated on 17/Mar/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({xg}\right)={f}\left({x}\right){g}\left({y}\right) \\ $$$${g}\left({xy}\right)={f}\left({x}\right)+{g}\left({y}\right) \\ $$$$\frac{{d}\left({fg}\right)}{{dx}}=? \\ $$ Answered by prakash jain last…
Question Number 818 by 123456 last updated on 17/Mar/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({xy}\right)={f}\left({x}\right){g}\left({x}\right)+{f}\left({y}\right){g}\left({y}\right) \\ $$$${g}\left({xy}\right)={f}\left({x}\right){g}\left({y}\right)+{f}\left({y}\right){g}\left({x}\right) \\ $$$$\frac{{d}\left({fg}\right)}{{dx}}=? \\ $$ Commented by prakash jain last…
Question Number 66342 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{U}_{{n}} =\int_{{n}} ^{{n}+\mathrm{2}} \:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{t}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dt}\:\:{prove}\:{that}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} =\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 806 by 123456 last updated on 16/Mar/15 $${if}\:{p}\left({x}\right)\:{is}\:{a}\:{polynomial}\:{and} \\ $$$${p}\left({x}\right){p}\left(\frac{\mathrm{1}}{{x}}\right)={p}\left({x}\right)+{p}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$$${p}\left(\mathrm{3}\right)=\mathrm{28} \\ $$$${then} \\ $$$${p}\left({x}\right)=? \\ $$$${p}\left(\mathrm{4}\right)=? \\ $$ Commented by 123456…
Question Number 805 by 123456 last updated on 17/Mar/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$${f}\left({xy}\right)={xf}\left({y}\right)+{yf}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 17/Mar/15…