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This is the Exam of Multivariate Calculus and its key important points are: Differentiable Function, Value, Directional Derivative, Direction, Decreases Most Rapidly, Tangent Plane, Graph of the Function, Equation, Extreme Values, Maximum
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MA 261 EXAM II Fall 1998 Page 1/
NAME
STUDENT ID # INSTRUCTOR
INSTRUCTIONS
A. −√ 52 B. − 1 C. −√ 37 D. 0 E. −√ 7
√x^ ey
(^3) dy dx.
A. 12 e B. 12 (e−1) C. 13 e D. 13 (e−1) E. e
0
∫ (^4) −x 2 0
∫ (^4) −x (^2) −y 2 0 z^2 dz dy dx
B.
0
∫ √ 4 −x 2 0
∫ (^4) −x (^2) −y 2 0 z dz dy dx C.
0
∫ (^4) −x^2 0
∫ (^4) −x^2 −y^2 0 z dz dy dx
D.
0
∫ √ 4 −x 2 0
∫ (^4) −x^2 −y^2 0 z dz dy dx
0
∫ √ 4 −y 2 0
∫ (^4) −x (^2) −y 2 0 z^2 dz dx dy
A. π 4 B. π 3 C. 27 π D. π 6 E. π 5
R cos(x^2 + y^2 )dA where R is the region in the xy-plane bounded by the circle x^2 + y^2 = π 2.