MATH 102 Final, Summer 2003

~} ae re RR eat AUVUGIT WISWHAING SVORISEVE remeron roreeemateeeand Mathematics 102 FINAL August 14, 2003, 8:00-9:30 Name: Important Instructions: 1. The entire solution of each problem must be written in the space beneath the problem. 2. You may lose up to 90% of the available credit for not providing essential explanations. 3.Do not separate these pages. 4.The pink booklets are merely a source of scrap paper. I will not read what is in them. You may take your pink booklet after the test. If you have any comments write them here: Good Luck! Total Some trigonometric formulas cos? x=1-sin? x, sec? x=1+tan?x cos? x= 5 (1+ 0052s), sin? x=5(0 —cos2x) AMERICAN UNIVERSITA LIBRARY ae TREE Problem 1. 5 pts Find the point in which the line x =1+ 2t, y=1+ 5t, z=3¢ meets the plane x+ytz=2. Problem 2. 5 pts Is the line x=1-2t, y=2+5t, z=—3f parallel to the plane 2x + y-z=8? Give reasons for your answer. eee tan ehiGas UNIVERSITET ; LIBRARY He BORE Problem 3. 5 pts Find parametrization for the line in which the planes x -2y+4z=2 and x+y-2z=5 intersect. OF BEIRUT Problem 4. 5 pts Find the plane determined by the intersecting lines L,: x=t, y=3-3t,2=-2-1 L,:x=l+s, y=4+s, z=-l+s. OF BEIRUT Problem 5. 5 pts Let v=5j—3k and u=i+j+k, Find a) the cosine of the angle between vy and u b) the scalar component of y in the direction of u c) the vector Proj 5 u d) juxy ee ener faatchicaS PSIVERS! j LIBAARY or BEIRCT Problem 6. 5 pts Find the center and radius of the sphere 2x? + 2y? +227 +4y-4z=9. IVEKSIT Lib ARY i GV RETRUT Problem 7, 5 pts Find a vector of magnitude 3 in the direction opposite to the direction of w=ij-1j-1é. 2 2 2 Problem 8. 5 pts Find an equation for the line through P(1,2) parallel to u = ~i-2j. TAS Fs SIVERSITD, LIBWKARY OF BEIRUT Problem 9. 5 pts sinx Evaluate [e cosxdx, Problem 10. 5 pts Evaluate fx? cos x dx. emt eae ee emnemee HST ty Lib waARY OF BEIRUT { wot Problem 11. 5 pts 3x? 412x411 Evaluate le . (x + 1) + 2)(x + 3) aan enen jamenic 6 CN(WERSIT LIBKARY OF BEIRUT Problem 12. 5 pts Evaluate [x? Inxde. Problem 13. 5 pts Evaluate [e cosGe' —2)dt.