Question

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

Answer 1

\[(x-2)\over \sqrt{x}-\sqrt{4-x}\]
right?

Answer 2

ty

Answer 3

o sorry

Answer 4

Did I rewrite the problem correctly?

Answer 5

yes

Answer 6

When you plug in 2 you get \[0 \over 0\], a indeterminate. SO we may apply L'Hopital Rule

Answer 7

or rationalize the denominator if you have not gotten to l'hopital yet

Answer 8

then cancel, plug in 2, and get the answer

Answer 9

i will write it if you like

Answer 10

manny are familiar with LHopital rule?

Answer 11

\[\frac{x-2}{\sqrt{x}-\sqrt{4-x}}=\frac{x-2}{\sqrt{x}-\sqrt{4-x}}\times
\frac{\sqrt{x}+\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}\]

Answer 12

sqrt(2) ans...

Answer 13

sqrt(2)= a.41421

Answer 14

\[=\frac{(x-2)(\sqrt{x}+\sqrt{x-4})}{2x-4}\]

Answer 15

\[=\frac{\sqrt{x}+\sqrt{4-x}}{2}\]

Answer 16

now replace x by 2 and get
\[\frac{2\sqrt{2}}{2}=\sqrt{2}\]

Answer 17

ty for the answers