Re: [微積] Limit 極限問題
爆掉example
consider f(x)= 0 , x=0
(x^2)sin(1/x) , x>0
then f is differentiable at [0,+oo) (用定義做可以做0那一點)
but f'(x) is not continuous at 0
Now
f(x) - f(0)
────── = f'(c)
x - 0
(x^2)sin(1/x) - 0
───────── = 2xsin(1/x) - cos(1/x)│x=c = 2csin(1/c) - cos(1/c)
x - 0
左右take lim x→0
左邊=f'(0)=0
右邊根本不存在
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