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If-lim-x-p-x-p-2-2p-2-p-2-x-2-L-find-lim-x-p-2p-3-x-p-3-x-p-




Question Number 83493 by jagoll last updated on 03/Mar/20
If lim_(x→p)  ((∣x+p∣^2 −∣2p∣^2 )/(p^2 −x^2 )) = L  find lim_(x→p)  ((∣2p∣^3 −∣x+p∣^3 )/(x−p))
$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{2}} −\mid\mathrm{2p}\mid^{\mathrm{2}} }{\mathrm{p}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{L} \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{2p}\mid^{\mathrm{3}} −\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{3}} }{\mathrm{x}−\mathrm{p}} \\ $$

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