MATH 102 Final, Fall 2001

American University of Beirut Math 102 Dr. H. Yamani Final Exam Name: Fall 2002 **k*kkCOOD LUCK**** ’ 1. Determine each of the following: a. J cos (sin”'x) dx V1-x? fact)? e* dx fx? dx x7 +4 2. What curve is given by the following parametric representations x =2+2 Cos2t y=3+3 Sin2t 3. Find the equation of the plane through the point (1,-1,3) parallel to the plane 3x+y+z=7 4. Find the area of a triangle with vertices P(1, 3, 2) , Q( 2,1,-1) , R(-3,1,5) 5. Find the angle between A=i-2j-2k and B= 6i+3j+2k 6. Find parametric equations for the line through P(1,2,0) and Q(1,3,-1). 7. Find the angle between y = (3/2)-x’ and y=x’ 8. Find the length of the curve r = cos*(6/3), 0<é<n/4 9. Find the area inside the graph of r= 1 and outside the graph of tT=1-cosé 10. Find the angle between the planes x = 7 and x+ y+ V2z2= -3 11.Test for convergence or divergence. State your reasons i dx Loe VOeF fo