Two functions f/g Uniform Continuity

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I was wondering if f and g are two uniformly continuous functions on a set such that g(x) is not zero is f/g uniformly continuous?


I have a feeling it is not but I can't seem to find a counter example.
 
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The function 1/x on ]0,1] should probably be a good counterexample...
 
But 1 is not considering a function f is it?
 
Take f(x)=1, the constant function, and g(x)=x...
 
If D is compact then f/g will be uniformly continuous on D right?
 
Yes. That's why I took the interval ]0,1].
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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