2z +i lim z→00 z +1 (2/z) + i 2 +iz = lim z→0 1+z = 2 since lim = 2. z→0 (1/z) + 1

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.3: Partial Fractions
Problem 2E
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EXAMPLES. Observe that
2z + i
lim
(2/z) + i
lim
z→0 (1/z) + 1
2 +iz
lim
z→0 1+z
= 2 since
2.
I+2 00+2
Furthermore,
2z3 – 1
lim
z→00 z2 + 1
.3
(1/z²) + 1
lim
z + z
lim
= O0
since
= 0.
||
z→0 (2/z³) – 1
z→0 2 – z3
Transcribed Image Text:EXAMPLES. Observe that 2z + i lim (2/z) + i lim z→0 (1/z) + 1 2 +iz lim z→0 1+z = 2 since 2. I+2 00+2 Furthermore, 2z3 – 1 lim z→00 z2 + 1 .3 (1/z²) + 1 lim z + z lim = O0 since = 0. || z→0 (2/z³) – 1 z→0 2 – z3
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