Limit approaching negative infinity

logaliciouz
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lim x( (x2 −2x+5)^(1/2)−|x−1|)
x→−∞

so far, the only way I have started the question is by multiplying for the conjugate but i cannot get it to simply to the answer which is -2 after that step.
 
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logaliciouz said:
lim x( (x2 −2x+5)^(1/2)−|x−1|)
x→−∞

so far, the only way I have started the question is by multiplying for the conjugate but i cannot get it to simply to the answer which is -2 after that step.

Show us what you did.
 

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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