设f(x)={sin3x/x,x＜0,a,x=0,xsin(1/x)+b,x＞0,求a，b的值，使f(x)在(-∞，+∞)的连续

设f(x)=
{sin3x/x,x＜0,
a,x=0,
xsin(1/x)+b,x＞0,
求a，b的值，使f(x)在(-∞，+∞)的连续．
【正确答案】：lim_x→0-f(x)=lim_x→0+[xsin(1/x)+b]=b， lim_x→0-f(x)=lim_x→0-(sin3x/x)=3， ∴a=3，b=3．