Question

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

Answer 1

[tex] \displaystyle \lim_{x \to \infty} (1+ \frac{x^2+1}{x^2-2} -1)^{x+3}=\\ = \lim_{x \to \infty} [(1+ \frac{3}{x^2-2})^{\frac{x^2-2}{3} ]^{(x+3)\frac{3}{x^2-2}}=e^0=1\\[/tex]