$\displaystyle \lim_{x\rightarrow-\infty}(\sqrt{x^{2}+x}-x) = ? $. this is how i solve this, but i know it's not true.. why? $\displaystyle

(\sqrt{x^{2}+x}-x)=\frac{(\sqrt{x^{2}+x}-x)\cdot(\sqrt{x^{2}+x}+x)}{(\sqrt{x^{2}+x}+x)}=$$\displaystyle \frac{x}{\sqrt{x^{2}+x}+x}$

$\displaystyle \frac{x}{x+x\cdot\sqrt{1+\frac{1}{x}}}=\frac{1}{1+ \sqrt{1+\frac{1}{x}}}$ so, $\displaystyle \lim_{x\rightarrow-\infty}f(x)=\frac{1}{2}

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