MATH 201 Final, Spring 2019
American University of Beirut · Calculus and Analytical Geometry III · 1 page
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Math 201—Final Exam
« Please write
Problem
Problem 2 (answer on page 2 of the booklet.)
(10 pts) Estimate ils 1 e-* de with an error of magnitude noe
over-estimate or an under-estimate?
Problem 3 (answer on pages 3, 4, 5. and 6 of the booklet.)
Consider the function f(x,y) = © “4 Set
a6 G). (8 pts), Find Domain and canada Devide i
d cide if Domain f is bounded or unk
oe nd all local maxima, local minima, and
4 pts) Find the absolute maximum and minim
Ben y* = 1 (i.e. the region is the set of all point (a,
- Gv) (9 pts) Integrate the peneuon J over the region
o=1,2—2, y=, and y= 7
Problem 4 (answer on pages 7 and 8 of the booklet.)
Evaluate ;
Wieck
(i) (9 pts) when D is the region in the first octant above the cone 2 = 4/a* Fa
plane z = 1;
(ii) (9 pts) when D is the region im the first octant above the cone 2 =
sphere:z + y?-+ 27 =4
Problems 5 > 6 are on the back side of the Paper.