Proficiency1 - Mathematical Basis Math Proficiency Test September 3 2009 1(10 points Compute x lim x x2 1 2(10 points Obtain all cubic roots of 1

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Unformatted text preview: Mathematical Basis Math Proficiency Test September 3, 2009 1. (10 points) Compute x+ lim x- x2 - 1 . 2. (10 points) Obtain all cubic roots of 1. 3. (10 points) Compute the following integral: x+3 dx. (x + 1)(x - 2) 4. (10 points) Compute the following integral: (y dx + x dy), C where C is the ellipse (x/a)2 + (y/b)2 = 1 and the integration is performed clockwise. 5. (10 points) Perform the Taylor series expansion of function f (x) = about point x = 1 up to (and including) quadratic term. x 1 ln(1 + x2 )dx 6. (10 points) Obtain extrema of function f (x) = 3x-2y subject to constraint x2 +y 2 = 4. 7. (10 points) Formulate the Stokes theorem. 8. (30 points) Obtain the general solution of the following ODEs: (a) (10 points) (b) (10 points) (c) (10 points) y = ex-y 1 + ex y (x) - 2y (x) + 5y(x) = 0 y (x) - 2y (x) + 5y(x) = x 1 ...
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This note was uploaded on 09/08/2010 for the course CHEME ech6847 taught by Professor Liu during the Fall '10 term at University of Illinois, Urbana Champaign.

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