evaluate limit lim as x approaches 2 of (x-2)/(Sqrt x)-(Sqrt (4-x))

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evaluate limit lim as x approaches 2 of (x-2)/(Sqrt x)-(Sqrt (4-x))

Mathematics
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\[(x-2)\over \sqrt{x}-\sqrt{4-x}\] right?
ty
o sorry

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Other answers:

Did I rewrite the problem correctly?
yes
When you plug in 2 you get \[0 \over 0\], a indeterminate. SO we may apply L'Hopital Rule
or rationalize the denominator if you have not gotten to l'hopital yet
then cancel, plug in 2, and get the answer
i will write it if you like
manny are familiar with LHopital rule?
\[\frac{x-2}{\sqrt{x}-\sqrt{4-x}}=\frac{x-2}{\sqrt{x}-\sqrt{4-x}}\times \frac{\sqrt{x}+\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}\]
sqrt(2) ans...
sqrt(2)= a.41421
\[=\frac{(x-2)(\sqrt{x}+\sqrt{x-4})}{2x-4}\]
\[=\frac{\sqrt{x}+\sqrt{4-x}}{2}\]
now replace x by 2 and get \[\frac{2\sqrt{2}}{2}=\sqrt{2}\]
ty for the answers

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