【求助】二李全书上一道多元函数微分学的题目请大家帮忙例1.17设当(x,y)=(0,0)时f(x,y)=0求:(1);(2)讨论f(x,y)在(0,0)处的可微性.【分析与求解】(1)当(x,y)=\=(0,0)时当(x,y)=(0,0)
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![【求助】二李全书上一道多元函数微分学的题目请大家帮忙例1.17设当(x,y)=(0,0)时f(x,y)=0求:(1);(2)讨论f(x,y)在(0,0)处的可微性.【分析与求解】(1)当(x,y)=\=(0,0)时当(x,y)=(0,0)](/uploads/image/z/10748821-13-1.jpg?t=%E3%80%90%E6%B1%82%E5%8A%A9%E3%80%91%E4%BA%8C%E6%9D%8E%E5%85%A8%E4%B9%A6%E4%B8%8A%E4%B8%80%E9%81%93%E5%A4%9A%E5%85%83%E5%87%BD%E6%95%B0%E5%BE%AE%E5%88%86%E5%AD%A6%E7%9A%84%E9%A2%98%E7%9B%AE%E8%AF%B7%E5%A4%A7%E5%AE%B6%E5%B8%AE%E5%BF%99%E4%BE%8B1.17%E8%AE%BE%E5%BD%93%EF%BC%88x%2Cy%EF%BC%89%3D%280%2C0%29%E6%97%B6f%28x%2Cy%29%3D0%E6%B1%82%EF%BC%9A%EF%BC%881%EF%BC%89%EF%BC%9B%EF%BC%882%EF%BC%89%E8%AE%A8%E8%AE%BAf%28x%2Cy%29%E5%9C%A8%EF%BC%880%2C0%EF%BC%89%E5%A4%84%E7%9A%84%E5%8F%AF%E5%BE%AE%E6%80%A7.%E3%80%90%E5%88%86%E6%9E%90%E4%B8%8E%E6%B1%82%E8%A7%A3%E3%80%91%EF%BC%881%EF%BC%89%E5%BD%93%EF%BC%88x%2Cy%EF%BC%89%3D%5C%3D%280%2C0%29%E6%97%B6%E5%BD%93%EF%BC%88x%2Cy%EF%BC%89%3D%280%2C0%29)
【求助】二李全书上一道多元函数微分学的题目请大家帮忙例1.17设当(x,y)=(0,0)时f(x,y)=0求:(1);(2)讨论f(x,y)在(0,0)处的可微性.【分析与求解】(1)当(x,y)=\=(0,0)时当(x,y)=(0,0)
【求助】二李全书上一道多元函数微分学的题目请大家帮忙
例1.17设当(x,y)=(0,0)时f(x,y)=0求:(1);(2)讨论f(x,y)在(0,0)处的可微性.【分析与求解】(1)当(x,y)=\=(0,0)时当(x,y)=(0,0)时,因为对于任意的x,f(x,0)=0,于是 由对称性得当(x,y)=\=(0,0)时同理.我的问题在于讨论起可微性,还请会的同学多多指教哈~因为偏导数连续可推出函数可微,故要讨论偏导数的连续性~即考察在点(0,0)处的连续性.下边是问题的重点:书上写道:“注意:于是 .就是这个”于是”愚笨的我是死活都看不明白,还请大家不吝赐教~
【求助】二李全书上一道多元函数微分学的题目请大家帮忙例1.17设当(x,y)=(0,0)时f(x,y)=0求:(1);(2)讨论f(x,y)在(0,0)处的可微性.【分析与求解】(1)当(x,y)=\=(0,0)时当(x,y)=(0,0)
这个实际上是利用不等式的缩放啊,原式>