. The derivative of w = f(z) at z = zo is given by f(zo+Az)-f(zo) Az f'(zo) = lim Az→0 = lim = Oz+z Show that f'(z) does not exist for any point z when z² (a) f(z) = Re z, (b) f(z) = Im z, and (c) f(z) Z ƒ(z) — ƒ(zo) 2-20 for z 0 and f(0) = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4. The derivative of w = f(z) at z = zo is given by
ƒ(zo+Az) – ƒ (zo)
Az
f'(zo) = lim
Az→0
-
Show that f'(z) does not exist for any point z when
z²
(a) f(z) = Re z, (b) f(z) = Im z, and (c) f(z)
Z
lim
2-20
ƒ(z) — ƒ (zo)
2- 20
for z 0 and f(0) = 0.
Transcribed Image Text:4. The derivative of w = f(z) at z = zo is given by ƒ(zo+Az) – ƒ (zo) Az f'(zo) = lim Az→0 - Show that f'(z) does not exist for any point z when z² (a) f(z) = Re z, (b) f(z) = Im z, and (c) f(z) Z lim 2-20 ƒ(z) — ƒ (zo) 2- 20 for z 0 and f(0) = 0.
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