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Course: MATH 3334, Fall 2008
School: U. Houston
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3334 Math Fall 2008 Professor William Ott Assignment 1: due Wednesday, September 3, 2008 (1) Prove that for x , y Rn , we have x y x y . This inequality is known as the reverse triangle inequality. Hint: use the triangle inequality. (2) Problem 1.5.2 from Marsden and Tromba (3) For x , y Rn and p &gt; 0, show that x + y p 2p ( x p + y p ). Hint: use the triangle inequality to show that x + y 2 max{ x , y...

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3334 Math Fall 2008 Professor William Ott Assignment 1: due Wednesday, September 3, 2008 (1) Prove that for x , y Rn , we have x y x y . This inequality is known as the reverse triangle inequality. Hint: use the triangle inequality. (2) Problem 1.5.2 from Marsden and Tromba (3) For x , y Rn and p > 0, show that x + y p 2p ( x p + y p ). Hint: use the triangle inequality to show that x + y 2 max{ x , y }, where max{ x , y } is the maximum of x and y . (4) Problem 1.5.10 Marsden from and Tromba (5) Prove that {(x, y) R2 : 3 < x2 + y 2 < 7} is open. (6) This problem shows that the boundary of a set can depend on the space into which the set is embedded. (a) Let a < b. Prove that for the interval (a, b] R, we have bdry((a, b]) = {a, b}. (b) Let ...

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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
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U. Houston - MATH - 3334
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