Complex analysis problem. I need help on the following two questions.

The definition of p_a(z) is given by the first paragraph, and the arc and line are described by the graph and two lines of words above it.

Let a be a positive real number. Define pa(2) = = =4:. This is the Cauchy distribution (with parameter a). If r is real, Pa(r) 2 0. One can check that Pa (x) = # tan(x/a), from which it follows that Pa(x) de = 1.This has two components: the line segment from -R to R, and the arc in the upper half-plane from R to -R. We call these two curves as line and are respectively. A picture is included below. We have set up the problem so that R lim Pai (2) Paz(x - z)dz = lim Pai (t)Paz(x - t)dt =/ Pai (t )Paz (x - t)dt 1400 line R-00 is the integral we want to compute. 1. Prove that lim Pai (2) Paz (x - 2) = 0. R+00 orc3. Use the Canning.r integral formula to show the integral of pl(z}pug{r z) amnnd alt (either along 71 or T2, depending on which you chose to enclose (111;) is given by 2?\": 1 I11 1 [1-2 _ 1 :12 fr 2:111? 7r (.1: alt}? + :1; 1r (1' 0511:}2 + a; Show also that the integral around 3: + .221; is equal to 27\": 1 [:1 1 {12 _ 1 m 7r(m +a2}2 +a 1:252:1 1r(:r:+agt'}2 +ag