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Question Number 80828 by jagoll last updated on 07/Feb/20

$$given$$$$\underset{x\to -\mathrm{\infty }}{\lim }[\sqrt{2x+p}-\sqrt{2x+1}]\times \sqrt{2x-p}=\frac{1}{4}p$$$$findp.$$

Commented by john santu last updated on 07/Feb/20

$$\underset{x\to -\mathrm{\infty }}{\lim }\sqrt{4x^2-p^2}-\sqrt{4x^2+(2-2p)x-p}=\frac{1}{4}p$$$$similarto$$$$\underset{x\to +\mathrm{\infty }}{\lim }\sqrt{4x^2-p^2}-\sqrt{4x^2+(2p-2)x-p}=\frac{1}{4}p$$$$\frac{0-(2p-2}{2.2}=\frac{p}{4}\Rightarrow p=\frac{2}{3}$$

Commented by jagoll last updated on 07/Feb/20

$$thx$$

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