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Question Number 5908 by sanusihammed last updated on 04/Jun/16 $${Solve}\:\: \\ $$$$\frac{{dy}}{{dx}}\:\:−\:{y}\:{tan}\:{x}\:\:=\:{y}^{\mathrm{2}} \:{tan}^{\mathrm{2}} \:{x} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Commented by 123456 last updated…
Question Number 5903 by sanusihammed last updated on 04/Jun/16 $${if}\:\:\:{x}^{{y}\:} \:=\:\:{e}^{\left({x}\:−\:{y}\right)} \\ $$$$ \\ $$$${find}\:\:{dy}/{dx} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Answered by uchechukwu okorie…
Question Number 71439 by Mr. K last updated on 15/Oct/19 $${If}\:{a}\:{seller}\:{could}\:{purchase}\:{goods}\:{at}\:{an} \\ $$$$\mathrm{8\%}\:{lower}\:{price}\:{by}\:{keeping}\:{the}\:{selling} \\ $$$${price}\:{fixed},\:{his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%.\:{So},\:{what}\:{is} \\ $$$${the}\:{value}\:{of}\:{x}? \\ $$ Commented by…
Question Number 5902 by Ashis last updated on 04/Jun/16 $${solve}\:{x} \\ $$$$\mathrm{6}^{\mathrm{2}{x}+\mathrm{4}} \:\:=\mathrm{3}^{\mathrm{3}{x}} \:\mathrm{2}^{{x}+\mathrm{8}} \\ $$ Commented by prakash jain last updated on 04/Jun/16 $$\mathrm{6}^{\mathrm{2}{x}}…
Question Number 5900 by 314159 last updated on 04/Jun/16 $${Prove}\:{that} \\ $$$${log}\:{n}!\:>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\ $$ Answered by Yozzii last updated on 05/Jun/16 $${Let}\:{for}\:{n}\in\mathbb{N},{n}\geqslant\mathrm{2},\: \\ $$$${P}\left({n}\right):\:{logn}!>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\…
Question Number 136969 by liberty last updated on 28/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{\left(\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{t}\right)\:\sqrt{\mathrm{sec}\:\mathrm{t}}}{\left(\mathrm{1}+\mathrm{sec}\:\mathrm{t}\right)^{\mathrm{2}} −\mathrm{2}}\:\mathrm{dt}\:=?\: \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\:\mathrm{E}\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}}…
Question Number 136968 by Eric002 last updated on 28/Mar/21 $$\left.\mathrm{1}\right)\int\frac{\mathrm{8}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}−\mathrm{6}\:}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{3}} \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\left(\mathrm{1}\right)\int\:\frac{\mathrm{8}}{\mathrm{x}^{\mathrm{3}}…
Question Number 136971 by Eric002 last updated on 28/Mar/21 $$\int{csc}^{\mathrm{4}} \left({x}\right)\:{cot}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$ Answered by Ñï= last updated on 28/Mar/21 $$\int{csc}\:^{\mathrm{4}} {x}\mathrm{cot}\:^{\mathrm{2}} {xdx}=−\int\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right)\mathrm{cot}\:^{\mathrm{2}}…