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How do I show that $\cos(x^2)$ is not a uniformly continuous function?

I try to choose some value of $x=\sqrt{n\pi}$ and $y=\sqrt{n\pi/2}$ so that $|x-y|<\delta$ and $|f(x)-f(y)>\epsilon$, but I got stuck when trying to state the relationship of x and y I picked and $\delta$ in order to make sure that it works for all $\delta$

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    As a first step, I highly recommend writing down the definition of uniformly continuous and taking its formal negation to discover what you need to show.2012-12-07
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    You'd be better off with $y=\sqrt{n\pi+\frac{\pi}{2}}$, and you could use (because $0): $|x-y|=y-x=\frac{y^2-x^2}{x+y}<\frac{y^2-x^2}{2x}$.2012-12-07
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    @JonasMeyer I got it! Thank you so much!2012-12-07
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    What's the domain? Continuous functions with compact domains are uniformly continuous, always.2012-12-07

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