- #1
nhrock3
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i need to prove that [TEX]\frac{1}{\sqrt{x}}[/TEX] is not uniformly continues in (0,1)
for epsilon=0.5
[TEX]|\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}|=|[/TEX][TEX]]\frac{\sqrt{y}-\sqrt{x}}{\sqrt{xy}}\frac{\sqrt{y}+\sqrt{x}}{\sqrt {y}+\sqrt{x}}|[/TEX][TEX]=|\frac{y-x}{(\sqrt{y}-\sqrt{x})\sqrt{xy}}|[/TEX]
i need to prove that the above exprseesion bigger then 0.5
but i don't know what x and y to choose
?
for epsilon=0.5
[TEX]|\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}|=|[/TEX][TEX]]\frac{\sqrt{y}-\sqrt{x}}{\sqrt{xy}}\frac{\sqrt{y}+\sqrt{x}}{\sqrt {y}+\sqrt{x}}|[/TEX][TEX]=|\frac{y-x}{(\sqrt{y}-\sqrt{x})\sqrt{xy}}|[/TEX]
i need to prove that the above exprseesion bigger then 0.5
but i don't know what x and y to choose
?