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Unformatted text preview: 1 1 . 00001 1 1 . 00001 1 1 . 00001 1 1 . 00001 1 has one positive eigenvalue and one negative eigenvalue. (Hint: = 0 is the other eigenvalue of the matrix.) I.D.# 5. Consider the polynomial equation a n x n + a n1 x n1 + + a = 0, where a ,a 1 ,...a n are integers with a 6 = 0 and a n 6 = 0. Show that if the equation is to have a rational root p/q , then p must divide a and q must divide a n exactly. I.D.# 6. Let a be a positive constant ( a > 0). Prove that the function f ( x ) = 1 /x 2 is uniformly continuous in the interval ( a, ). I.D.# 7. Let a 1 ,a 2 ,a 3 ,... be positive numbers. (a) Prove that if n =1 a n converges then n =1 a n a n +1 converges. (b) Prove that the converse of the statement in part (a) is false. I.D.# 8. Show that Z x 2 ex 2 dx = 1 2 Z ex 2 dx....
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 Fall '08
 Feinberg,E

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