2. Determine the convergence or divergence of each improper integral by com- paring it to simpler improper integrals whose convergence or divergence is known or can be found directly. (a) 1 + sin (x) (b) 1 + In(x) 2:2 3. Suppose that in the course of Emmy's job as a civil engineer at Hanford, she needs to find out how much radioactive cesium was present in the mixture in a certain tank when it was first filled exactly 12 years ago. Suppose Q(0) is the number of pounds of radioactive cesium that was initially in the tank 12 years ago, at time 7 = 0. The amount of cesium in the tank at any time 7' 2 0 is the amount that remains to decay, which for some constant k is equal to Q (t) = ke-0.023t dt (a) If Emmy measures 0.95 1b of cesium in the tank now, how much cesium was in the tank when it was first filled 12 years ago? (b) In another location in the tank farm, there is a tank that was filled with a different, known mixture that contained 1.5 1b of radioactive cesium when the tank was filled. However, there is no record of when this tank was filled. Emmy measures 0.85 1b of cesium in the tank now. How long ago was the tank filled