Limiti?

si copiato da un vecchio post, ma va sempre bene

  1. \displaystyle \lim_{x \to \infty} \left ( \frac{x^2+1}{x^2} \right )^{x^2+1}
  2. \displaystyle \lim_{x \to \infty} \left ( \frac{x+8}{x-2} \right )^x
  3. \displaystyle \lim_{x \to 0} \frac{\sqrt{2} - \sqrt{1+ \cos x}}{\sin^2 x}
  4. \displaystyle \lim_{x \to 0} \frac{\sqrt{1+ \sin x} - \sqrt{1- \sin x}}{x}
  5. \displaystyle \lim_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x+ \sqrt{x+ \sqrt{x}}}}
  6. \displaystyle \lim_{x \to 0} \frac{1- \cos x \sqrt{\cos 2x}}{x^2}
  7. \displaystyle \lim_{x \to \frac{\pi}{2}} \frac{1- \sin^3 x}{\cos^2 x}
  1. \displaystyle \lim_{x \to \infty} \left ( \frac{x^2+1}{x^2} \right )^{x^2+1}