Limit Problem: Solving (x+2)/(x3+8) without a Calculator

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I can't seem to figure this out, its very simple. I am just unsure as to how to o about it. Could someone please solve it, showing the method. No calculator either. thanks

Lim as x-> -2 ; (x+2) / (x3+8)
 
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Problems like this usually involve factoring the polynomials involved. Try doing that.
 
yeah, like already said, you need to factor the denominator. I assume you are familiar with the sum of cubes:

a^3+b^3=(a+b)(a^2-ab+b^2) this is all you need to factor the denominator.
 
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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