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Unformatted text preview: 3. (6 points) Use diﬀerentials to estimate the amount of tin in a closed tin can with diameter 8cm and height 12 cm if the tin is .04 cm thick. 4. (6 points) Calculate the directional derivative of f ( x, y ) = x 2 y in the direction of < 3 , 4 > at the point (1 , 2). 5. (6 points) Show that f ( x, y ) = xy is a solution to the diﬀerential equation ∂ 2 f ∂x 2 + ∂ 2 f ∂y 2 = 0 . Bonus: (3 points) Find a function f so that f xx 6 = 0 and f satisﬁes LaPlace’s equation. 6. (8 points) For Z 1 Z 4 4 x f ( x, y ) dy dx sketch the region of integration and change the order of the integration. Bonus: (4 points) Evaluate the integral Z 1 Z y 3 y e x 2 dx dy....
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This test prep was uploaded on 04/12/2008 for the course MATH 211 taught by Professor Crow during the Fall '07 term at Gettysburg.
 Fall '07
 Crow
 Math

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