Пределы подробное решение
Lim x →1 (x^2-1)/(√x-1)

lim (x->1) (x^a-x^b)/(x^1/5-1)=(1^a-1^b)/(1^(1/5)-1)=0/0 -> lim(x->1) (d/dx)(x^a-x^b)/(d/dx)(x^1/5-1)=

= lim(x->1) 5*(1/(x^1/5))*(ax^a-bx^b) = lim(x->1) (5*(ax^a-bx^b))/lim( x->1) (x^1/5)=

= lim(x->1) 5*(a-b)/1 =5*(a-b)

Ответ: 5(a-b)