Which of the dicontinuities are removable?

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Homework Statement

Find the x values if any for which x is not continuous.Which of the dicontinuities are removable?

Homework Equations

f(x)=1/(x^2+1)

The Attempt at a Solution

Its unfactorable at the bottom ,i tried to factor it.Would this mean there are no discontinuities?
 
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Are you sure you wrote down the problem correctly. It is undefined when the denominator is zero but x^2 + 1 is never zero. Or maybe the answer is that it is continuous everywhere.
 
thanks
 

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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