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…
Question Number 66341 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}^{\mathrm{3}} }{\:\sqrt{\left(\mathrm{1}+\left(\frac{{k}}{{n}}\right)^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$ Commented by Prithwish sen…
Question Number 66324 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}^{{n}} \:+{ln}\left({n}\right)} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66322 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{f}\left({x}\right)=\left({cosx}\right)^{\frac{\mathrm{1}}{{x}}} \:\left(\:\mathrm{1}\right)\:\:{prove}\:{that}\:{f}\left({x}\right)\sim\mathrm{1}−\frac{{x}}{\mathrm{2}}+\frac{{x}^{\mathrm{2}} }{\mathrm{8}}\:\:\left(\:{x}\rightarrow\mathrm{0}\right) \\ $$$$\left(\mathrm{2}\right){ptove}\:{that}\:{f}^{'} \left({x}\right)\sim−\frac{\mathrm{2}}{\pi}\:{e}^{\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right){ln}\left({cosx}\right)} \:\:\left({x}\rightarrow\frac{\pi}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy…