<s>[INST] How to calculate $\lim \limits_{x \to 0}{\frac{\sqrt{1 + x + x^2} - 1}{x}}$? I try to calculate $\lim \limits_{x \to 0}{\frac{\sqrt{1 + x + x^2} - 1}{x}}$. I've got $\frac{\sqrt{1 + x + x^2} - 1}{x} = \sqrt{\frac{1}{x^2} + \frac{1}{x} + x} - \frac{1}{x}$ but I don't know what to do next.
 [/INST] Hint: $\dfrac{\sqrt{1 + x+ x^2} -1}{x} = \dfrac{x + x^2}{x (\sqrt{1 + x+ x^2} + 1)} = \dfrac{1+x}{\sqrt{1 + x+ x^2} + 1}$
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