April 24, 2012Prelim 3Math 1106Please show your reasoning and all your work.This is a 90 minuteexam. Calculators are not needed or permitted. Good luck!Unless specifically requested, answers on this exam NEED NOTbe simplified or completely numerical. Arithmetic expressions arefine. Ordinarily, answers likeln125,3x2(x4-1)-4x3(x3+ 1)(x4-1)2,12(4x3)(x4+ 1).5are completely acceptable.Problem 1) (27 Points)1a)Evaluate206x2-2x+ 4dx.1b)Evaluate211-2x2dx.1c)Evaluate and express as simply as possible (without a calculator)1
Problem 2) (12 Points)Calculate∂z∂yin each of the following cases:2a)z=x7y3+xy2.
Problem 3) (20 Points)3a)Find the general solution of the differential equationdxdt=3t22x.1