Question

1. lim $frac{ x^{2} +1}{ x^{2} -1}$
2. lim$frac{ x^{2} -2x-1}{ x^{2} -9}$
3. $frac{4 x^{2} }{ x^{2} -1}$

Answer 1

$lim_{x to infty} x^2(1+1/x^2)/x^2(1-1/x^2)=1$
$lim_{x to infty} x^2(1-2/x-1/x^2)/x^2(1-9/x^2)=1$
$lim_{x to infty} 4x^2/x^2(1-1/x^2)=4$