Question Number 7667 by upendrakishor99@gmail.com last updated on 08/Sep/16 $$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\left[{x}−{x}^{\mathrm{2}} \mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\right] \\ $$ Answered by FilupSmith last updated on 08/Sep/16 $$=\alpha−\alpha^{\mathrm{2}} \mathrm{log}\left(\mathrm{1}+\frac{\mathrm{1}}{\alpha}\right) \\ $$…
Question Number 7665 by upendrakishor99@gmail.com last updated on 08/Sep/16 $$\frac{{d}}{{dx}}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$ Answered by Rasheed Soomro last updated on 08/Sep/16 $$\frac{{d}}{{dx}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\left(\mathrm{1}/\mathrm{2}\right)−\mathrm{1}}…
Question Number 7655 by Tawakalitu. last updated on 07/Sep/16 $$\left(\frac{\mathrm{8}}{{x}}\right)^{{x}} \:=\:\:{x}^{\mathrm{2}} \\ $$$$ \\ $$$${Show}\:{that}\:\:{x}\:=\:\mathrm{4} \\ $$ Commented by FilupSmith last updated on 07/Sep/16 $$\mathrm{trial}\:\mathrm{and}\:\mathrm{error}…
Question Number 7608 by Tawakalitu. last updated on 06/Sep/16 $${If}\:\:{x}\:=\:{cos}\Theta\:−\:{sin}\Theta \\ $$$${and}\:\:{y}\:=\:{cos}\mathrm{2}\Theta \\ $$$${Show}\:{that},\:\: \\ $$$${y}\:=\:{x}\sqrt{\mathrm{2}\:−\:{x}^{\mathrm{2}} } \\ $$ Commented by sou1618 last updated on…
Question Number 73137 by behi83417@gmail.com last updated on 06/Nov/19 Commented by behi83417@gmail.com last updated on 06/Nov/19 $$\mathrm{A}\overset{\blacktriangle} {\mathrm{B}C},\:\mathrm{is}\:\mathrm{equilateral}\:\mathrm{with}:\:\mathrm{AB}=\mathrm{a} \\ $$$$\mathrm{BDFG},\mathrm{is}\:\mathrm{rectangle}. \\ $$$$\mathrm{find}:\:\mathrm{S}_{\mathrm{B}\overset{\blacktriangle} {\mathrm{H}F}} ,\mathrm{in}\:\mathrm{terms}\:\mathrm{of}:\:\:\mathrm{a}\:. \\…
Question Number 7600 by Rohit last updated on 05/Sep/16 $${solve}\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\mid<\mathrm{3}\:\:{give}\:{solution} \\ $$ Answered by Yozzia last updated on 05/Sep/16 $$\mid{u}\left({x}\right)\mid<{a}\Rightarrow−{a}<{u}\left({x}\right)<{a}. \\ $$$$\therefore\mid\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 138661 by mr W last updated on 16/Apr/21 Commented by mr W last updated on 16/Apr/21 $${proof}\:{for}\:{Q}\mathrm{138519} \\ $$ Commented by mr W…
Question Number 138658 by ajfour last updated on 16/Apr/21 Commented by ajfour last updated on 16/Apr/21 $${Find}\:{maximum}\:{area}\:{of}\:\bigtriangleup{AOB}. \\ $$$${a}=\mathrm{1}. \\ $$ Commented by mr W…
Question Number 7544 by Tawakalitu. last updated on 03/Sep/16 Commented by sou1618 last updated on 03/Sep/16 $${x}={OA} \\ $$$${OB}=\sqrt{{x}^{\mathrm{2}} +\mathrm{144}} \\ $$$$\Delta{ABO}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{12}{x} \\ $$$$\Delta{AOB}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{3}\left(\mathrm{12}+{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{144}}\right)…
Question Number 138554 by cherokeesay last updated on 14/Apr/21 Answered by mr W last updated on 14/Apr/21 Commented by mr W last updated on 14/Apr/21…