高数多元函数微分学偏导数内容,急求解答,谢谢.
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高数多元函数微分学偏导数内容,急求解答,谢谢.
![高数多元函数微分学偏导数内容,急求解答,谢谢.](/uploads/image/z/2746771-43-1.jpg?t=%E9%AB%98%E6%95%B0%E5%A4%9A%E5%85%83%E5%87%BD%E6%95%B0%E5%BE%AE%E5%88%86%E5%AD%A6%E5%81%8F%E5%AF%BC%E6%95%B0%E5%86%85%E5%AE%B9%2C%E6%80%A5%E6%B1%82%E8%A7%A3%E7%AD%94%2C%E8%B0%A2%E8%B0%A2.)
Df(0,0)/Dx = lim(x→0)[f(x,0)-f(0,0)]/x = lim(x→0)(0-0)/x = 0,
Df(0,0)/Dy = lim(y→0)[f(0,y)-f(0,0)]/y
= lim(y→0){ysin[1/(0²+y²)]/y}
= lim(y→0)sin(1/y²)
不存在.
Df(0,0)/Dy = lim(y→0)[f(0,y)-f(0,0)]/y
= lim(y→0){ysin[1/(0²+y²)]/y}
= lim(y→0)sin(1/y²)
不存在.