Question

$lim_{n to infty} ( frac{x+2 x^{2} }{ x^{2} -4})^{x}$

Answer 1

$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} =$$lim_{x to infty} ( frac{2+ frac{1}{x} }{1 - frac{4}{x^2} })^{x}=2^infty=infty$