Help with $\lim_{x\rightarrow +\infty} (x^2 - \sqrt{x^4 - x^2 + 1})$ $\lim_{x\rightarrow  +\infty} (x^2 - \sqrt{x^4 - x^2 + 1}) = ?$
I don't know how to solve the indetermination there... is it possible to rearrange the expression in brackets in order to use L'Hospital or Taylor Series?

You may write
$$
x^2 - \sqrt{x^4 - x^2 + 1}=\frac{(x^2)^2 - (x^4 - x^2 + 1)}{x^2 + \sqrt{x^4 - x^2 + 1}}=\frac{1 - \frac{1}{x^2}}{1 + \sqrt{1 - \frac{1}{x^2} + \frac{1}{x^4}}} \to \frac12
$$ as $x \to +\infty$.
