Question Number 110086 by john santu last updated on 27/Aug/20
$$\:\:\frac{\spadesuit{JS}\spadesuit}{\bigstar\blacksquare.\bigstar} \\ $$$${If}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}\mid{ax}\mid−\mathrm{3}{a}^{\mathrm{2}} }{\:\sqrt{{x}}−\sqrt{{a}}\:}\:=\:{P}\:,\:{with}\:{a}>\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mid{ax}\mid−{a}^{\mathrm{2}} }{{x}−{a}}\:{is} \\ $$$$\_\_\_ \\ $$$$\:\left({a}\right)\:\frac{\mathrm{3}{P}}{\mathrm{4}\sqrt{{a}}}\:\:\:\:\:\:\left({b}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}\sqrt{{a}}}\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{8}{P}}{\mathrm{3}\sqrt{{a}}} \\ $$$$\:\:\left({d}\right)\:\frac{\mathrm{4}{P}}{\mathrm{3}\sqrt{{a}}\:}\:\:\:\:\left({e}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}{a}} \\ $$
Answered by bemath last updated on 27/Aug/20
Commented by john santu last updated on 27/Aug/20
$${great}.. \\ $$