Infinite limit of absolute value

tsumi
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Homework Statement



i just want to know one value that i can't find anywhere, and would love some help

Homework Equations



<br /> \lim_{x\rightarrow\ -\infty}|x|}

The Attempt at a Solution


thanks
 
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If you look at the graph of y = |x|, the limit is pretty obvious.
 
As x goes to -infinity, it must be negative! For negative x, |x|= -x. What is the limit \lim_{x\rightarrow -\infty} -x?
 
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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