推 pp20624:謝 雖然我英文很差看不太習慣@@ 61.227.116.152 05/26 17:03
※ 引述《pp20624 (kk)》之銘言：
: 5x^2 y
: ------ , (x,y) ≠(0,0)
: x^3+y^3
: let f(x,y){
: 0 , (x,y) = (0,0)
: prove that
: a. f (0,0) exists ,and
: x
f(0+h,0)-f(0,0)
fx exsists iff the lim ----------------- exsists
h->0 h
both limits for fx and fy are 0, exsists.
: b. fis not differentiable at (0.0)
: 有請大大 謝謝
f is differentiable if fx and fy is continuous
but as you can see, (x^3+y^3) will be squared after you differentiate,
having a discontinuity at (0,0)
so f is not differentiable at (0,0)
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