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Question Number 110086 by john santu last updated on 27/Aug/20

  ((♠JS♠)/(★■.★))  If lim_(x→a) ((x^2 +2∣ax∣−3a^2 )/( (√x)−(√a) )) = P , with a>0  then the value of lim_(x→a) ((2x^2 −∣ax∣−a^2 )/(x−a)) is  ___   (a) ((3P)/(4(√a)))      (b) ((3P)/(8(√a)))     (c) ((8P)/(3(√a)))    (d) ((4P)/(3(√a) ))    (e) ((3P)/(8a))

$$\:\:\frac{\spadesuit{JS}\spadesuit}{\bigstar\blacksquare.\bigstar} \\ $$ $${If}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}\mid{ax}\mid−\mathrm{3}{a}^{\mathrm{2}} }{\:\sqrt{{x}}−\sqrt{{a}}\:}\:=\:{P}\:,\:{with}\:{a}>\mathrm{0} \\ $$ $${then}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mid{ax}\mid−{a}^{\mathrm{2}} }{{x}−{a}}\:{is} \\ $$ $$\_\_\_ \\ $$ $$\:\left({a}\right)\:\frac{\mathrm{3}{P}}{\mathrm{4}\sqrt{{a}}}\:\:\:\:\:\:\left({b}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}\sqrt{{a}}}\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{8}{P}}{\mathrm{3}\sqrt{{a}}} \\ $$ $$\:\:\left({d}\right)\:\frac{\mathrm{4}{P}}{\mathrm{3}\sqrt{{a}}\:}\:\:\:\:\left({e}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}{a}} \\ $$

Answered by bemath last updated on 27/Aug/20

Commented byjohn santu last updated on 27/Aug/20

great..

$${great}.. \\ $$

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