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Math_200_December_2005

# Math_200_December_2005 - MATH 200 Name Marks[10 1 Page 2 of...

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December 20, 2005 MATH 200 Name Page 2 of 10 pages Marks [10] 1. One side of a right triangle is measured to be 3 with a maximum possible error of ± 0 . 1, and the other side is measured to be 4 with a maximum possible error of ± 0 . 2. Use the differential or linear approximation to estimate the maximum possible error in calculating the length of the hypotenuse of the right triangle. Continued on page 3

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December 20, 2005 MATH 200 Name Page 3 of 10 pages [10] 2. Assume that f ( x, y ) satisfies Laplace’s equation 2 f ∂x 2 + 2 f ∂y 2 = 0. Show that this is also the case for the composite function g ( s, t ) = f ( s t, s + t ). That is, show that 2 g ∂s 2 + 2 g ∂t 2 = 0. You may assume that f ( x, y ) is a smooth function so that the Chain Rule and Clairaut’s Theorem on the equality of the mixed partials derivatives apply. Continued on page 4
December 20, 2005 MATH 200 Name Page 4 of 10 pages [10] 3. You are standing at a location where the surface of the earth is smooth. The slope in the southern direction is 4 and the slope in the south-eastern direction is 2. Find the slope in the eastern direction.

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Math_200_December_2005 - MATH 200 Name Marks[10 1 Page 2 of...

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