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。