Unformatted text preview: 2. (25 points) ±ind the center of gravity ( x, y ) of the region R which is the top half of the ellipse x 2 + (1 / 4) y 2 = 1. (You may appeal to symmetry, and you may use the fact that R has area π .) 3. (a) (15 points) The amount of work required to stretch a certain spring 6 centimeters from equilibrium is 1000 ergs. How much work is required to stretch the spring an additional 6 centimeters? (b) (10 points) Sketch the curve described in polar coordinates by the equation r = cos(3 θ ). 4. (a) (10 points) Suppose w = 12 i and z = 2 e 6 i . Plot w and z in the complex plane. Compute  w  ,  z  and  wz  . (b) (3 points) Write an equation which relates the exponential, sine and cosine functions. (c) (3 points) Compute the radius of convergence of the complex power series ∑ ∞ n =0 (12 i ) n z n . (d) (4 points) ±ind real numbers a, b such that a + ib = ∞ X n =0 ± 1 2 + i 2 ² n ....
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 Fall '07
 Hamilton
 Math, Calculus, Derivative, Complex number, Euler's formula

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