Question

Подробно Помогите найти предел?
1,$y= frac{ 3x^{2}-10x+8 }{ x^{2} -4}$ , при х=2
2,$y= frac{ sqrt{x} -1}{ x^{2} -1}$ , при х=1

Answer 1

$lim_{x to 2} frac{3(x- frac{4}{3})(x-2) }{(x-2)(x+2)}= lim_{x to 2} cfrac{3(x-4/3)}{x+2} = 2/4 =0.5$

$lim_{x to 1} cfrac{ (sqrt{x}-1)( sqrt{x} +1) }{(x^2-1)( sqrt{x} +1)} = lim_{x to 1} cfrac{x-1}{(x-1)(x+1)( sqrt{x} +1)}$
$=lim_{x to 1} cfrac{1}{(x+1)( sqrt{x} +1)}= cfrac{1}{2*2}=0.25$