Question

Ajutor! Imi trebuie cat mai repede

Answer 1

$\lim_{x \to \infty} ( \sqrt{ x^{2} -3x+1}-x)= \lim_{x \to \infty} \frac{( \sqrt{ x^{2} -3x+1}-x)( \sqrt{ x^{2} -3x+1}+x) }{ \sqrt{ x^{2} -3x+1}+x) } \\ = \lim_{x \to \infty} \frac{ x^{2} -3x+1- x^{2} }{ x( \sqrt{1- \frac{3}{x}+ \frac{1}{ x^{2} } }+1 )} = \lim_{x\to \infty} \frac{x(-3+ \frac{1}{x}) }{x( \sqrt{1- \frac{3}{x}+ \frac{1}{x^2} }+1) } = \\ = \frac{-3}{2}$