المحاضرة الرابعة عشر

( Limits ) ( ت?????? ت ( ا ????? ا
w0 z0 w = f (z)
Lim f (z) = w0 z0 z
? > 0
? > 0
Lim f (z) = w0 z0 z
? > 0
0 < ?z - z0? ? z < ? ? > 0
<
? ? > 0 , ?? > 0 , 0 < < ? < ?
z w0 w = f (z)
z0
? z0 ? w0
N (w0 , ? ) N ( z0 , ? )
z z0
f (z) – w0
u
v
w.
( Limits ) ( ت?????? ت ( ا ????? ا
w0 z0 w = f (z)
Lim f (z) = w0 z0 z
? > 0
? > 0
Lim f (z) = w0 z0 z
? > 0
0 < ?z - z0? ? z < ? ? > 0
<
? ? > 0 , ?? > 0 , 0 < < ? < ?
z w0 w = f (z)
z0
? z0 ? w0
N (w0 , ? ) N ( z0 , ? )
z z0
f (z) – w0
u
v
w.
0
??
y
x
z0
0
z. w 0
z – z0 w – w0
z z0
51
z ? > 0 ? > 0
0 < < ?
< ?
< ?
< ?
< ?
< ?
<
أي أن >
? ?
Z - (2i – 1)
2Z + 3 – ( 4i+ 1)
f (z) - wo
2Z + 3 – ( 4i+ 1)
2Z – 4i+ 2
2( z – (2i – 1 ) )
Z – ( 2i – 1 )
Z – Z0
lim(2 3) 4 1 2 1
? ? ?
? ?
z i
z i
2
?
2
?
2
0
??
y
x
z0
0
z. w 0
z – z0 w – w0
z z0
51
z ? > 0 ? > 0
0 < < ?
< ?
< ?
< ?
< ?
< ?
<
أي أن >
? ?
Z - (2i – 1)
2Z + 3 – ( 4i+ 1)
f (z) - wo
2Z + 3 – ( 4i+ 1)
2Z – 4i+ 2
2( z – (2i – 1 ) )
Z – ( 2i – 1 )
Z – Z0
lim(2 3) 4 1 2 1
? ? ?
? ?
z i
z i
2
?
2
?
2