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