Lời giải:

• \( m \leq 0 \): không thỏa.
• \( m > 0 \):

\(\lim_{x \to +\infty} y = \lim_{x \to +\infty} \frac{x \left( 1 - \sqrt{m + \frac{2}{m^2}} \right)}{x \left( 1 + \frac{1}{x} \right)} = 1 - \sqrt{m}\)

\(\lim_{x \to -\infty} y = 1 + \sqrt{m}\)

Vậy \( m > 0 \).