Question

Найдите предел
lim( √(n^2+1)-√(n^2-1) )
n→+∞

Answer 1

$displaystyle lim_{n to infty} big( sqrt{n^2+1} - sqrt{n^2-1}big)= lim_{n to infty} frac{n^2+1-n^2+1}{ sqrt{n^2+1}+ sqrt{n^2-1} }=\ \ \ =2lim_{n to infty} frac{ frac{1}{n} }{ sqrt{1 + frac{1}{n^2} }+ sqrt{1- frac{1}{n^2} } } =0$