设函数f(x)=x-sinx/|x|能否补充说明f(0)使函数在x=0处连续

Question

设函数f(x)=x-sin x/|x| 能否补充说明f(0) 使函数在x=0处连续

Answer 1

for x0
f(x) = x - sin1
lim(x->0+)f(x) = -sin1
lim(x->0-)f(x) = sin1 ≠ lim(x->0+)f(x)
f(x) is discontinuos at x=0
不能说明f(0) 使函数在x=0处连续