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Calculus III - Test #2 Solutions, March 2002, Exams of Advanced Calculus

Baddi University of Emerging Sciences and TechnologiesAdvanced Calculus

The solutions to calculus iii test #2 held on march 21, 2002. The test covers topics such as finding local and absolute extreme values, calculating iterated integrals, and finding volumes of solids. Functions involved include polynomial functions, exponential functions, and elliptic paraboloids.

Typology: Exams

2012/2013

Uploaded on 03/16/2013

pahal
pahal 🇮🇳

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MA 227: Calculus III
Test #2, March 21, 2002
Time limit: 100 min.
Your name:
Your student ID:
1. Find the local maximum and minimum values and saddle points of the function
f(x, y) = x2+y2+1
x2y2.
20 points
2. Find the local maximum and minimum values and saddle points of the function
f(x, y) = eycos x.
20 points
pf3

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MA 227: Calculus III Test #2, March 21, 2002

Time limit: 100 min. Your name:

Your student ID:

  1. Find the local maximum and minimum values and saddle points of the function

f (x, y) = x^2 + y^2 +

x^2 y^2

20 points

  1. Find the local maximum and minimum values and saddle points of the function

f (x, y) = ey^ cos x.

2

  1. Find the extreme values (absolute minimum and maximum) of the function

f (x, y) = 2x^2 + 3y^2 − 4 x

on the region defined by the inequality x^2 + y^2 ≤ 16. 20 points

  1. Find the absolute minimum and maximum values of the function f (x, y, z) = x^2 + y^2 + z^2 subject to the constraint x^4 + y^4 + z^4 = 1.