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Prove f(x)=1/x is not uniformly continuous at (0, infinity) and prove that is is uniformly continuous at [a, infinity] for every real #, a.?

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  • Prove f(x)=1/x is not uniformly continuous at (0, infinity) and prove that is is uniformly continuous at [a, infinity] for every real #, a.?


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Prove that the function defined by $f(x) = \sin(1/x)$ is not uniformly continuous on the interval $(0,1)$. Hint: Consider for example $x = 1/2nπ$ and $y ...
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Positive: 54 %
which works for every x 0 2R. f ... The function f(x) = 1=xis not uniformly continuous on (0 ... We are going to need the notion of uniform continuity to ...
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Positive: 51 %

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Solutions to Selected Homework Problems 6.1. Choose either f(x) = ex or f(x) = lnx and prove it is not uniformly continuous. ... f(x) = x x+1 x ≥ 0, x
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Positive: 54 %
... f(x) is uniformly continuous. We know every ... f(x) = \frac{1}{x}[/tex] is unif. continuous on ... a > 0[/tex], they prove it with: We note [tex]x,y ...
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Positive: 49 %
... = 0 if x is irrational, prove that x is not continuous at ... The function f(x) = 1 / x is continuous on (0 ... If f(x) is uniformly continuous in ...
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Positive: 35 %
x2 is not uniformly continuous on (0,1). If f(x) = 1 x2 were ... so f(x) is not uniformly continuous on (0,1 ... Prove that if f is uniformly continuous ...
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Positive: 12 %

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