lim 230 (Rez) ---1-2-1- 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
follow the definition, proof in the Delta-Epilson method
![By Def 3.1: given E>0 there exists f= $(E) >0 s.t. for all 7 with
we have IP(z) - (notivo) |<ε.
0²1Z-Zo)<S
1 Im z), 'Rez) < | Rez +i Imz) = 1Z1, we get:
Since for any Z E C
1 v(x, y)- vol, lu(x, y) - uol < | u(x, y) - Up + i (v(x, y) - Yo)|
Tu(x, y) + iv (x, y) - (40 +ivo)]
]+(z) - (40+ivo) | < E
12
Thus
Tulx, y)-Hol< e and Iv(x,y) - Vok<ε
CHECK: IZ-Zol is the distance from (x, y) to (xo, yo) in IR²
u(x, y) = Uo
and lime V(x,y) = V₂.
(x,y) → (xo, yo)
lim
(x, y) →→(xo, yo)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F033c0d82-90fb-4c58-9b03-1325bfffdb8d%2F8842f5e0-2445-4e50-8955-ac6957a0c655%2F2ouu7s5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:By Def 3.1: given E>0 there exists f= $(E) >0 s.t. for all 7 with
we have IP(z) - (notivo) |<ε.
0²1Z-Zo)<S
1 Im z), 'Rez) < | Rez +i Imz) = 1Z1, we get:
Since for any Z E C
1 v(x, y)- vol, lu(x, y) - uol < | u(x, y) - Up + i (v(x, y) - Yo)|
Tu(x, y) + iv (x, y) - (40 +ivo)]
]+(z) - (40+ivo) | < E
12
Thus
Tulx, y)-Hol< e and Iv(x,y) - Vok<ε
CHECK: IZ-Zol is the distance from (x, y) to (xo, yo) in IR²
u(x, y) = Uo
and lime V(x,y) = V₂.
(x,y) → (xo, yo)
lim
(x, y) →→(xo, yo)
Transcribed Image Text:c) lim
240
(Rez)
IZ-1
0
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