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Please help with this limit! i don’t understand it.

Please help with this limit! i don’t understand it.-example-1
User Tacoshy
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1 Answer

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Factorize the numerator as a difference of squares:


x-s=(\sqrt x)^2-(\sqrt s)^2=(\sqrt x-\sqrt s)(\sqrt x+\sqrt s)

Then


\displaystyle\lim_(x\to s)(x-s)/(\sqrt x-\sqrt s)=\lim_(x\to s)(\sqrt x+\sqrt s)=\boxed{2\sqrt s}

User Sectornitad
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