求两道复变函数极限【请用定义证明】:(1)lim(z -> z0 ) z^2 = z0^2(2)lim(z -> 1-i
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求两道复变函数极限
【请用定义证明】:
(1)lim(z -> z0 ) z^2 = z0^2
(2)lim(z -> 1-i ) [x+i(2x+y)] = 1 + i ,其中z = x + iy
【请用定义证明】:
(1)lim(z -> z0 ) z^2 = z0^2
(2)lim(z -> 1-i ) [x+i(2x+y)] = 1 + i ,其中z = x + iy
![求两道复变函数极限【请用定义证明】:(1)lim(z -> z0 ) z^2 = z0^2(2)lim(z -> 1-i](/uploads/image/z/5027027-59-7.jpg?t=%E6%B1%82%E4%B8%A4%E9%81%93%E5%A4%8D%E5%8F%98%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E3%80%90%E8%AF%B7%E7%94%A8%E5%AE%9A%E4%B9%89%E8%AF%81%E6%98%8E%E3%80%91%EF%BC%9A%EF%BC%881%EF%BC%89lim%28z+-%3E+z0+%29+z%5E2+%3D+z0%5E2%EF%BC%882%EF%BC%89lim%28z+-%3E+1-i)
(1)对于∀ε>0,∃δ=min{1,ε},当|z-z0|<δ时,
![](http://img.wesiedu.com/upload/2/51/251b0ed15cb7493769a3a43484e9c5a0.jpg)
(2)对于∀ε>0,∃δ=ε,当|z-(1-i)|<δ时,有|x-1|<δ,|y+1|<δ,此时,
![](http://img.wesiedu.com/upload/a/40/a400a1edcd719540dce6fecb2725d7b2.jpg)
![](http://img.wesiedu.com/upload/2/51/251b0ed15cb7493769a3a43484e9c5a0.jpg)
(2)对于∀ε>0,∃δ=ε,当|z-(1-i)|<δ时,有|x-1|<δ,|y+1|<δ,此时,
![](http://img.wesiedu.com/upload/a/40/a400a1edcd719540dce6fecb2725d7b2.jpg)
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