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標題: differentiability [打印本頁]

作者: kwoklap 時間: 09-5-15 06:45 PM 標題: differentiability

let
g(x,y) =  (x^2+y^2)sin(1/(x^2+y^2)^0.5)  where x^2+y^2  =/= 0
g(x,y) = 0  where x^2+y^2  = 0

this function is not differentiable at (0,0) since the partial derivatives are
not continuous there.
我想問點解partial derivatives除左存在之外仲要連續,因為我諗番係one variable case : f(x) = x^2 sin(1/x) where x =/=0  and f(x) = 0  where x =0
f(x) is differentiable at x = 0 但f'(x)在x=0 不連續

幫幫手,就考final,急到瀨屎

作者: Naozumi 時間: 09-5-16 08:43 AM

我諗你攪錯左, theorem只係話partial derivative contiunous => differentiable
至於partial derivative not continuous, 冇講到任何野喎

作者: kwoklap 時間: 09-5-17 04:45 PM

thx!

問多條

$\\lim_{(x,y)\\to (0,0)} \\frac{\\left |x \\right | + \\left | y \\right |}{\\sqrt{x^2+y^2}}$

[ 本帖最後由 kwoklap 於 2009-5-17 04:46 PM 編輯 ]

作者: Naozumi 時間: 09-5-17 04:51 PM

Not exist

case 1 : y = 0
limit = 1

case 2: y = x
limit = sqrt(2)

作者: kwoklap 時間: 09-5-17 04:55 PM

我之前用polar做都唔exist,冇ans對所以問下

作者: kwoklap 時間: 09-5-17 07:25 PM

個prof.問過surface area of (x/a)^2+(y/b)^2+(z/c)^2=1
我怕會出所以計下,but條數太過messy,計計下走火入魔放棄左

,我想問個ans係乜,如果可以show埋個step黎睇下

[ 本帖最後由 kwoklap 於 2009-5-17 07:27 PM 編輯 ]

作者: kwoklap 時間: 09-5-18 01:29 PM

都係唔使la,我係網上找到個ans好鬼複雜,我估9成都唔出,個prof想玩我地

作者: Naozumi 時間: 09-5-18 06:51 PM

擺明玩你,都冇closed form

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