Why Does the Limit of \(x^2 - \frac{1}{x}\) as \(x\) Approaches 0 Not Exist?

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[SOLVED] Just one more limit problem.

Homework Statement


Find the limit


Homework Equations


\lim_{x \rightarrow 0} (x^2 - \frac{1}{x})


The Attempt at a Solution


I got does not exist for this limit. This is since, when you break it down to two parts, the 1/x is undefined at 0.
 
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That's correct.
 
allright, thank you
 
The fact that a function is undefined at a point does not imply the limit does not exist at that point.
 
It is infinite on both sides of the point, it doesn't exist.
 

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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