Re: [多變] 兩題多變數函數的極限
: 如圖
: 兩題解到一半都卡卡的
1.
tanθ
lim ------ = 1
θ→0 θ
tan(x - y)
So lim ------------ = 1 as x - y can be made arbitrary small if
(x,y)→(2,2) x - y (x,y) is close enough to (2,2)
(*) Another possible answer
tan(x - y)
lim ------------ doesn't exist since the function is not defined
(x,y)→(2,2) x - y in any neighborhood of (2,2) along the line x=y.
It depends on the definition of the limit.
2.
x^3 - xy^2 r^3 cosθcos(2θ)
By writing ----------- in polar form we get -------------------
x^2 + y^2 r^2
which is r cosθcos(2θ) when (x,y)≠(0,0) and its absolute value is
less than r. So the limit is
-1 π
cos 0 = ---
2
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.217.35.77
※ 編輯: suhorng 來自: 61.217.35.77 (04/15 11:39)
→
04/15 11:58, , 1F
04/15 11:58, 1F
→
04/15 11:59, , 2F
04/15 11:59, 2F
→
04/15 12:25, , 3F
04/15 12:25, 3F
推
04/15 13:09, , 4F
04/15 13:09, 4F
討論串 (同標題文章)
