Question

$\lim_{x \to \infty} \sqrt {x^{2} -2x+1} - \sqrt{ x^{2} -1$
Cum se rezolva acest exercitiu

Answer 1

[tex] \lim_{n \to \infty} \frac{(x^2-2x+1)-(x^2-1)}{ \sqrt{x^2-2x+1}+ \sqrt{x^2-1} } =\\ = \lim_{n \to \infty} \frac{x(-2+ \frac{2}{x}) }{x( \sqrt{1- \frac{2}{x} + \frac{1}{x^2} } + \sqrt{1- \frac{1}{x^2} } )} =\frac{-2}{1+1} =-1[/tex]