Question 13Question 14Question 15Question 16 Use the definition f'(zo) = lim (2) - f (Zo) of the derivative to find the6.Find the image of the semi-infinite strip x20, 0s ysT under thetransformation w= e², and label the corresponding portions of the boundaries.7.Use the ɛ,8 - definition of a limit to prove the following limit.lim (az + b) = azo +b, for complex numbers a and b with a + 0.8.Use Limit Laws to evaluate the following limits:iz -1422a) limb)lim (z? -4z+2+ 5i)c)lim2+0 (z – 1)2z+2+i4z° +zlim9.Prove the following limit.= 002+ 0 z+i10.Use the precise ɛ,8 - definition of continuity to prove that if f(z) is continuousat zo then f(z) is continuous at zo -11.z- z0derivative of f(z) =for z +0.12.Use differentiation formulas from calculus to find f'(z).a)f(2) = 3z2 – 2z +4ib)f(z) = (2z+5)(z+i)³az +b13.Find the derivative of the function T(z) =where a, b, c, d are complexcz +d°numbers such that ad – bc + 0. When is T'(z) = 0?14.Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point.а)f(z) = Zb)f(2) = e*e¯iy15.Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is onlydifferentiable at z = 0 and find the value of f'(0).16.Use the Cauchy-Riemann Equations to show that f(z) = z is differentiable forall z and find f'(z).

Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Answered: 13. Find the derivative of the function…

13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is T'(z) = 0? where a, b, c, d are complex

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

Question 13 Question 14 Question 15 Question 16

Use the definition f'(zo) = lim (2) - f (Zo) of the derivative to find the
6.
Find the image of the semi-infinite strip x20, 0s ysT under the
transformation w= e², and label the corresponding portions of the boundaries.
7.
Use the ɛ,8 - definition of a limit to prove the following limit.
lim (az + b) = azo +b, for complex numbers a and b with a + 0.
8.
Use Limit Laws to evaluate the following limits:
iz -1
422
a) lim
b)
lim (z? -4z+2+ 5i)
c)
lim
2+0 (z – 1)2
z+2+i
4z° +z
lim
9.
Prove the following limit.
= 00
2+ 0 z+i
10.
Use the precise ɛ,8 - definition of continuity to prove that if f(z) is continuous
at zo then f(z) is continuous at zo -
11.
z- z0
derivative of f(z) =
for z +0.
12.
Use differentiation formulas from calculus to find f'(z).
a)
f(2) = 3z2 – 2z +4i
b)
f(z) = (2z+5)(z+i)³
az +b
13.
Find the derivative of the function T(z) =
where a, b, c, d are complex
cz +d°
numbers such that ad – bc + 0. When is T'(z) = 0?
14.
Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point.
а)
f(z) = Z
b)
f(2) = e*e¯iy
15.
Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only
differentiable at z = 0 and find the value of f'(0).
16.
Use the Cauchy-Riemann Equations to show that f(z) = z is differentiable for
all z and find f'(z).

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