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好吧问答库 > 设f(x)=x*sin(1⼀x) ,x不等于0;f(x)=0 x=0,则f(x)在x=0处的可导性和连续性是什么望指教谢谢啦急用

设f(x)=x*sin(1⼀x) ,x不等于0;f(x)=0 x=0,则f(x)在x=0处的可导性和连续性是什么望指教谢谢啦急用

2025年03月15日 18:14

有1个网友回答

网友（1）：

1. 连续
因为 lim（x→0）f（x）=lim（x→0）xsin（1/x）=0=f（0）
2. 不可导
因为lim（x→0）[f（x）-f（0）]/x=lim（x→0）xsin（1/x）/x
=lim（x→0）sin（1/x）极限不存在。

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