Math_200_April_2006

# Math_200_April_2006 - Marks[15 1 MATH 200 Name Page 2 of 9...

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April 11, 2006 MATH 200 Name Page 2 of 9 pages Marks [15] 1. If two resistors of resistance R 1 and R 2 are wired in parallel, then the resulting resistance R satisFes the equation 1 R = 1 R 1 + 1 R 2 . Use the linear or di±erential approximation to estimate the change in R if R 1 decreases from 2 to 1 . 9 ohms and R 2 increases from 8 to 8 . 1ohms .

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April 11, 2006 MATH 200 Name Page 3 of 9 pages [10] 2. Assume that the directional derivative of w = f ( x, y, z )atapo int P is a maximum in the direction of the vector 2 i j + k , and the value of the directional derivative in that direction is 3 6. (a) Find the gradient vector of w = f ( x, y, z )at P .[5% ] (b) Find the directional derivative of w = f ( x, y, z )at P in the direction of the vector i + j
MATH 200 Name Page 4 of 9 pages [10] 3. Use the Second Derivative Test to Fnd all values of the constant c for which the function z = x 2 + cxy + y 2 has a saddle point at (0 , 0). Continued on page 5

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Math_200_April_2006 - Marks[15 1 MATH 200 Name Page 2 of 9...

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