[latex] \lim_{n \to \infty} ( \frac{x+2 x^{2} }{ x^{2} -4})^{x} [/latex]

[latex]\lim_{x \to \infty} ( \frac{x+2 x^{2} }{ x^{2} -4})^{x} =\lim_{x \to \infty} ( \frac{2 x^{2}+x }{ x^{2} -4})^{x}=\lim_{x \to \infty} ( \frac{x^{2}(2+ \frac{1}{x}) }{ x^{2}(1 - \frac{4}{x^2} })^{x} =[/latex][latex]\lim_{x \to \infty} ( \frac{2+ \frac{1}{x} }{1 - \frac{4}{x^2} })^{x}=2^\infty=\infty[/latex]