EXAM 3
Math 232
April 30, 2007
Name
1. Locate and classify all critical points for the function xye−x2
−y2
2. Find the absolute extrema of the function f(x, y) = x2+y2−2x−4yon the region bounded
by y=x,y= 3 and x= 0.
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Exam 3 Question Paper - Calculus III | MATH 232, Exams of Advanced Calculus
Material Type: Exam; Professor: Diener; Class: Calculus III; Subject: Mathematics; University: Christian Brothers University; Term: Spring 2007;
Typology: Exams
Pre 2010
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EXAM 3
Math 232 April 30, 2007
Name
- Locate and classify all critical points for the function xye−x (^2) −y 2
- Find the absolute extrema of the function f (x, y) = x^2 + y^2 − 2 x − 4 y on the region bounded by y = x, y = 3 and x = 0.
- Compute a Riemann sum for f (x, y) = x + 2y^2 on the region bounded by 0 ≤ x ≤ 2 and − 1 ≤ y ≤ 1. Use n = 4 and evaluate at the midpoint.
- Find the center of mass for the lamina whose area is bounded by x = y^2 and x = 1. The lamina has a density function of ρ(x, y) = y^2 + x + 1.