Is the Function f(x)=1/(1-1/x) Defined at x=0?

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[SOLVED] value of 1/(1-1/0) at 0

Homework Statement


Is the function
f(x)=\frac{1}{1-\frac{1}{x}}​
defined at x=0?

Homework Equations


The Attempt at a Solution


Since we have division by zero in the denominator, I'm assuming that it isn't. Am I correct?
 
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I would agree.
 
Yes, 1/0 is NOT defined. You don't have to "assume" anything!
 

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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