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f-f-n-2n-f-n-

Question Number 32743 by naka3546 last updated on 01/Apr/18 $${f}\:\left({f}\:\left({n}\right)\right)\:\:=\:\:\mathrm{2}{n} \\ $$$${f}\:\left({n}\right)\:\:=\:\:? \\ $$ Commented by abdo imad last updated on 03/Apr/18 $${if}\:{f}\:{is}\:{a}\:{polynomial}\:{fof}\left({x}\right)=\mathrm{2}{x}\:\Rightarrow{f}^{,} \left({f}\left({x}\right)\right){f}^{'} \left({x}\right)=\mathrm{2}\:\Rightarrow{y}^{,}…

Question-32710

Question Number 32710 by mondodotto@gmail.com last updated on 31/Mar/18 Answered by MJS last updated on 01/Apr/18 $${f}\left({x}\right)={a}\left({x}+\mathrm{1}\right)\left({x}−\mathrm{4}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${a}×\mathrm{1}×\left(−\mathrm{4}\right)=\mathrm{3} \\ $$$${a}=−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${f}\left({x}\right)=−\frac{\mathrm{3}}{\mathrm{4}}{x}^{\mathrm{2}}…

Question-32709

Question Number 32709 by mondodotto@gmail.com last updated on 31/Mar/18 Answered by MJS last updated on 31/Mar/18 $$\mathrm{log}_{\mathrm{2}} \:\mathrm{3}=\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{ln}\:\mathrm{2}}=\mathrm{p} \\ $$$$\mathrm{log}_{\mathrm{3}} \:\mathrm{2}=\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{ln}\:\mathrm{3}}=\mathrm{p}^{−\mathrm{1}} \\ $$$$\mathrm{2}^{{p}^{{x}} } =\mathrm{3}^{{p}^{−{x}}…

Question-32666

Question Number 32666 by naka3546 last updated on 30/Mar/18 Commented by abdo imad last updated on 30/Mar/18 $${let}\:{put}\:{A}_{{n}} =\:\frac{\left({n}+\mathrm{6}\right)^{\frac{{n}+\mathrm{6}}{{n}}} \:−{n}^{\frac{{n}+\mathrm{6}}{{n}}} }{\left({n}+\mathrm{3}\right)^{\frac{{n}+\mathrm{3}}{{n}}} \:−\:{n}^{\frac{{n}+\mathrm{3}}{{n}}} } \\ $$$${A}_{{n}}…