设函数f(x)在x=x0处的导数不存在,则曲线y=f(x)在x=x0处的极限不存在?

不一定
e.g
f(x) =|x|
f'(0+) = 1,f'(0-) =-1
=> f'(0) does not exist
but
lim(x->0)f(x) = 0