(b) Prove that each of the following functions is continuous, stating any rules that you use. (i) s(2) - 1 (Re z > 0) e -1 (ii) f(2) = 2 (Im z > 0) (iii) f(2) = (-1) (z € C)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Solve a part of posible solve b too
(a) Determine whether or not the sequence
(2+ i)" + (1+ i)"
(1 – 2i)" + 2"
n = 1,2, ...,
converges, and if it converges, then find its limit.
(b) Prove that each of the following functions is continuous, stating any
rules that you use.
1
e - 1
(i) S(2)
(Re z > 0)
(ii) f(2) = 2' (Im z > 0)
(iii) f(2) = (-1) (z € C)
Transcribed Image Text:(a) Determine whether or not the sequence (2+ i)" + (1+ i)" (1 – 2i)" + 2" n = 1,2, ..., converges, and if it converges, then find its limit. (b) Prove that each of the following functions is continuous, stating any rules that you use. 1 e - 1 (i) S(2) (Re z > 0) (ii) f(2) = 2' (Im z > 0) (iii) f(2) = (-1) (z € C)
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