Showing a limit doesn't exist using Delta/Epsilon

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Homework Statement



Prove that the limit as x approaches 0 of 1/x does not exist

Homework Equations


Delta epsilon definition


The Attempt at a Solution


I'm really stuck
 
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Use the following definition:

\forall L;\exists\epsilon>0;\forall\delta>0;\exists x:|x-a|<\delta and|f(x)-L|<\epsilon
 
I know that is the definition for a limit, but I am unsure how to disprove it
 
Well first assume that : \lim_{x\rightarrow0}\frac{1}{x}=L
 
lepton123,
Please read your private mails. You have started two threads without showing any effort. If you continue doing so, it could result in a ban from this forum.

mtayab,
Please, no more hints until lepton123 shows some effort.
 

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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