Keep getting an indeterminate answer for limit

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Homework Statement


Determine the limit:

lim as x->-2 [1/(1+x)+1]/[2x+x^2]


Homework Equations





The Attempt at a Solution



I can't seem to work around it, I keep getting an indeterminate answer.
 
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thomasrules said:

Homework Statement


I can't seem to work around it, I keep getting an indeterminate answer.
Do you mean an indeterminate answer or an infinite one?
 
No i think indeterminate...
 
\lim_{x\rightarrow -2}\frac{\frac{1}{1+x}+1}{2x+x^2}

Yes, Indeterminate: 0/0. But you shouldn't "keep" getting an inderminate answer. Have you tried L'Hopital's rule?
 
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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