b. (3 pts) For R > 0, let Sr be the semicircular arc which is the intersection of the circle {z : [2] = R} and the close

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B 3 Pts For R 0 Let Sr Be The Semicircular Arc Which Is The Intersection Of The Circle Z 2 R And The Close 1 (55.2 KiB) Viewed 20 times

b. (3 pts) For R > 0, let Sr be the semicircular arc which is the intersection of the circle {z : [2] = R} and the closed upper half plane {z : Im(2) >0}. Show that 1 lim dz=0. SR (22 + 2)2 Hint: use the estimate Sc fdz| = (max{\f(z)|: Z E C}). (length(C)). . C. (4 pts. Show all work for full credit.) Use Cauchy's Integral Formula (previous page, with n = 1), and an appropriate contour (part of which is SR from b.) to give an exact value for the real improper integral Lot tadi. 1 dr. 24 + 4.x2 + 4