MATH 102 Final, Fall 2012
American University of Beirut · Calculus and Analytical Geometry II · 10 pages · Mr. Hassan Yamani
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Dr. H Yamani
Final Exam
(Maximum Score=200pts)
Name:
Circle Section:
Sec.1: Tuesday 9:30am, Sec. 2: Tuesday 11am, Sec.3: Tuesday 8am
Problem 1)
a) Find the focus and directrix of the parabola. y²=12x
b) Find the equation of the ellipse with foci (+-2,0) and vertices (+-5,0).
c) Find the foci, vertices, asymptotes of hyperbola
.
Problem 1 (/15)
Problem 2 (/40)
Problem 3 (/20)
Problem 4 (/20)
Problem 5 (/20)
Problem 6 (/30)
Problem 7 (/20)
Problem 8 (/15)
Problem 9 (/10)
Problem 10 (/10)
Math201
Fall2012
Problem 2)
a) Find the distance from point S (2,2,2) to the line with parametric equations x =1+2t , y=1+6t , z=3+t. -∞< t <+∞
b) Find the distance from point S (1,2,3) to plane x + y + z = 2.
c) Find the equation of a plane through point (3,4,5) and normal to the line of intersection of the planes 2x-y + z = 2
and 2x + y-2z = 3.
d) Find an equation of the plane through the points A (1,2,3), B (3,2,1) and normal to plane 4x – y + 2z = 7.
Problem 3)
a) Write u = 2i – j + 3k as a sum of a vector parallel to v = 2i – j + 2k and a vector orthogonal to v.
b) Find area of a triangle with vertices P (-3,1,-3), Q (2,-1,5), R (1,1,1).
Problem 4)
a)
b)
Problem 5)
a)
b)
Problem 6) Test the following integrals for convergence or divergence only. Explain
a)
b)
c)
Problem 7) Determine the unit tangent vector T, the principal unit normal vector N, the unit binormal vector B, and the curvature
K.
r (t) = (sint) i + (cost) j +t k
Problem 8) r (t) = (tsint + cost) i + (sint - tcost) j ; t > 0.
Without finding T and N, write the acceleration of the curve in the form a=aTT + aNN.
Problem 9) Find the length of the curve r(t) = (tsint+cost) i + (sint - tcost) j. 0 ≤ t ≤ 2π
Problem 10) Find the parametric equations for the line with endpoints A(1,3,7) and B(4,6,9).