lim & ltx→0-& gt； E [(x- 1)/x] = +∞，lim < x→0->f(x)= 0；

Lim & ltx→0+>E [(x- 1)/x] = 0, then lim

Then x = 0 is jump discontinuity, which belongs to the first discontinuity;

lim & ltx→ 1 & gt； E [(x- 1)/x] = 1, and lim < x→1>; f(x) = ∞，

Then x = 1 is infinite discontinuity and belongs to the second kind of discontinuity. Choose C.