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Mathematics (MA) 2011
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The distinct eigenvalues of the matrix
are
The minimal polynomial of the matrix
is
Which of the following is the imaginary part of a possible value of ln(√i) ?
Let f : C → C be analytic except for a simple pole at z = 0 and let g : C → C be analytic. Then, the value of Res (f(z)g(z)) / Res f(z) as z → 0 is
Let I = ∮C (2x2 + y2)dx + eγ dy, where C is the boundary (oriented anticlockwise) of the region in the first quadrant bounded by y = 0, x2 + y2 = 1 and x = 0. The value of I is
The series ∑n=1^∞ xn/nm, x > 0, is convergent on the interval