00 (a) Solve for a: f 9 a: 00 l "3) Find the largest interval of values for R such that f R 9+$2 RE d3: a tt-m ' 33:19 [g[w)]odlverges to torp- m (c) For 30 # 0, consider I MI) '12. Fill in the following: I) m E m - f h(1:) Elm diverges to for p - o m m (d) Determine that f (a? elm converges to for p a Note: You can earn partial credit on this problem. Given eu du 2 , find the exact values of the following improper integrals. 97-2 EFE e 2 dx = 972 re 2 da = ADO 92 2 e 2 dx = 0 A DO .3 92-2 2 dx = 0 A DO 4 92- 2 T e 2 da = 0N -6 -4 -2 Lo 2 4 6 X -2 -4 Shown above is a graph of the functions y = f(2) = - _4 arctan(x) 2 2 + 1 and y = g(x) = - Define the functions Fi(t), F2(t), Gi(t) and G2(t) by F1(t ) = [ f(x) du, Gi(t) = (x) da F2 (t ) = ( f(x) da Gz (t) = / (2 ) da Evaluate each of the following improper integrals and limits. b) lim Fi(t) c) lim F2(t) e) lim G1(t) f) lim G2(t)In the theory of probability, the piecewise-defined function 0, for .7: