Đáp án:
`lim_(xto1)\frac{sqrt(5-x^3)-\root{3}{x^2+7}}{x^2-1}=-11/24`
Giải thích các bước giải:
`lim_(xto1)\frac{sqrt(5-x^3)-\root{3}{x^2+7}}{x^2-1}`
`=lim_(xto1)\frac{sqrt(5-x^3)-2+2-\root{3}{x^2+7}}{x^2-1}`
`=lim_(xto1)\frac{sqrt(5-x^3)-2}{(x-1)(x+1)}+\frac{2-\root{3}{x^2+7}}{(x-1)(x+1)}`
`=lim_(xto1)(\frac{-(x^2+x+1)}{(x+1)(sqrt(5-x^3)+2)}-frac{1}{4+2\root{3}{x^2+7}+\root{3}{(x^2+7)^2}})`
`=-11/24`
Vậy `lim_(xto1)\frac{sqrt(5-x^3)-\root{3}{x^2+7}}{x^2-1}=-11/24`