MATH 102 Final, Summer 2002
American University of Beirut · Calculus and Analytical Geometry II · 1 page
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Summer 2woQ
American University of Beirut Math 102
Dr. H. Yamani Final Exam
Name:
*kEX GOOD LUCK****
1. Evaluate
: . 2
lim (x+e>)*
Nor
2. Find dy/dx
y= (In xX )! (Inxy
3. Determine each of the following:
dx
4+x°
Idx
9 — 4x?
w/2
| sin(In x) dx
1
|-2x +4 dx
(x”- 1)?
x” dx
2
VO -x
4. Find the area shared by the circles r=4cos @ and r=4sin 0
5. Graph the polar curve r= [+ 2 Cos 0
6. Find the equation of the plane through the point (-1,6.0) perpendicular to the
line x=-l+t.y=6-2t. 2=3t
7. Find the angle between u=i-2j—-2k and v= 6i+ 3j+2k
8. Determine whether the following converges or diverges:
et
AMERIC |S UNIVERSIT
Lhie RY
OF et