Suppose that f(x) = u(x, y) + iv(x, y) and zo = xo + iyo. Prove that lim f(2)=uo + ivo 2-20 if and only if lim u(x, y) = (x,y) →(xo,yo) = Uo and lim (x,y) →(xo,yo) u(x, y) = vo.
Suppose that f(x) = u(x, y) + iv(x, y) and zo = xo + iyo. Prove that lim f(2)=uo + ivo 2-20 if and only if lim u(x, y) = (x,y) →(xo,yo) = Uo and lim (x,y) →(xo,yo) u(x, y) = vo.
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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Transcribed Image Text:Suppose that f(z) = u(x, y) + iv(x, y) and zo = xo + iyo. Prove that
lim f(z) = uo + ivo
if and only if
02-2
lim u(x, y) = uo
(x,y) →(xo,yo)
and
lim
(x,y) →(xo,yo)
u(x, y) =
= vo.
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