Calculus 3 Practice Exam 4

# Calculus 3 Practice Exam 4 - ) at the point (-2 , 1) in the...

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Math 209 Practice Exam 4 1. Sketch a graph of the domain of f ( x, y ) = x + y . 2. Sketch the level curves z = 0 , 1 , 2 for z = x + y . 3. Find the equation of the tangent plane to the surface graph of f ( x, y ) = x sin( y ) at the point (1 , 0). 4. Find the total diﬀerential dz of z = x sin( y ). 5. Use the chain rule to ﬁnd dz dt given that z = y x , x = t 2 and y = 2 t + 1 6. Use the chain rule to ﬁnd ∂z ∂t when s = 2 , t = 1 given z = x + xy - y 3 , x = 4 t + s and y = st - t 2 7. Use partial derivatives to ﬁnd the implicit derivative dy dx given 3 x 2 y 3 - xy + y 2 = 0. 8. Find the directional derivative D u f ( x, y
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Unformatted text preview: ) at the point (-2 , 1) in the direction of the vector <-3 , 4 > for f ( x, y ) = x 2 y-x + 2 y . 9. Find the amount of the greatest slope of the surface graph of f ( x, y ) = x 2 y-x + 2 y at the point (-2 , 1). In what direction is the steepest slope? (specify a vector for the direction) 10. Use the second derivative test to ﬁnd all local minimum, maximum and saddle points on the surface f ( x, y ) = x 2 + xy 2-y ....
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## This note was uploaded on 04/18/2008 for the course MATH 209 taught by Professor Bales during the Spring '08 term at Tuskegee.

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