Question

lim_{x rightarrow 1-} (sqrt{2x}\left| 1-x \right|)div(x ^{2}-1)

Answer 1

\[\lim_{x \rightarrow 1-} (\sqrt{2x}\left| 1-x \right|)\div(x ^{2}-1) \]

Answer 2

ya

Answer 3

For 0<x<1 we have \[\frac{\sqrt{2x}|1-x|}{x^2-1}=-\frac{\sqrt{2x}(1-x)}{(x-1)(x+1)} = - \frac{\sqrt{2x}}{x+1} \]
Now you can insert x=1, so the limit is \[-\sqrt{2}/2\]

Answer 4

Oh sorry, erase the sign after the first equality! But that doesn't change anything.