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Author: Tinku Tara

f-R-R-g-R-R-d-fg-dx-df-dx-dg-dx-d-f-2-dx-df-dx-df-dx-d-g-2-dx-

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…

lim-x-0-x-2-cos-x-3sin-x-x-5-

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}}…

List-all-primes-p-for-which-p-2-and-p-4-are-also-primes-

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}.…