Right limit = lim (x-> 0+)f(x)= lim(x-& gt； 0+)(x/x)= 1

∵ Left limit ≠ Right limit

∴f(x) has no limit when x=0;

2. Left limit = lim (x->; 2-)f(x)= lim(x-& gt； 2-)(x+2)=4

Right limit = lim (x-> 2+)f(x)= lim(x-& gt； 2+)[ 1/(x-2)]=+∞

∵ Left limit ≠ Right limit

∴f(x) has no limit when x=2;

Fourth, ∫ lim (x->; ∞)[(x^2+ 1)/(x+ 1)-x-b]= 1/2

= = & gtlim(x->； ∞)[(( 1-a)x^2-(a+b)x+( 1-b))/(x+ 1)]= 1/2

= = & gtlim(x->； ∞) [(1-a) x-(a+b)+(1-b)/x)/(1+1/x)] =1/2 (numerator and denominator divided by x

= = & gt 1-a=0，-(a+b)= 1/2

∴a= 1,b=-3/2。