Limit of 3x/(5-x) as x approaches 5+ in Calculus

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Homework Statement



lim x->5+

3x/(5-x)


Homework Equations





The Attempt at a Solution


Is this a straight forward solution,
-infinity?
Because 3*5=15, and if x approaches 5 from the positive side, it means that (5-x)=-0.000000000001
So, 15/-000000000000.1 = -infinity
 
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yep, that's right. I don't know why the somebody chose to make such a trivial example into a problem, but whatever.
 
I expected to have some tricks in this problem...
 

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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