This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 185 SOLUTIONS OF HW VII (1) (41.5)(30pts) By triangle inequality, Logz z 2  ln R  +  i  R 2 < ln R + R 2 since z = ln R + i where z = Re i and < < . (N.B.  ln R  = ln R since R > 1.) Hence, Z C R Logz z 2 dz Z C R Logz z 2 dz < 2 R ln R + R 2 = 2 ln R + R Moreover, lim R 2 (ln R + ) R = lim R 2 (1 /R ) 1 = 0 by LHospitals rule, we can conclude that lim R Z C R Logz z 2 dz = 0 NOTICE. If you finish to solve the problem, you need to check WHAT YOU HAVE PROVEN. Even though you write the same sentence appear ing the problem, it is important because it can clarify your assertion. (2) (43. 5)(30pts) First we may replace the branch < < by / 2 < < 3 / 2 since 1 is not defined in Logz and change of the branch cut does not affect to the result in this situation. So, we can use the antiderivative z 1+ i 1+ i of z i ....
View
Full
Document
This note was uploaded on 09/01/2010 for the course MATH 185 taught by Professor Lim during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Lim
 Math

Click to edit the document details