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Course: MATH 414, Spring 2008School: Cornell
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414 Math Spring 2005 Homework Assignment 4 Due Thursday 24 February Section 9.3.7: 6, 7, 12, 13, 15, 17, 20; plus the problem below. 1. This problem completes the proof of the Stone-Weierstra Theorem given in class. Dene a sequence of polynonial functions {pn }n0 on [1, 1] by recursion as follows: = p0 0, x2 p2 (x) n pn+1 (x) = pn (x) + 2 for n 0. (a) Show that |x| pn+1 (x) = |x| pn (x) 1 |x| + pn (x) 2 for...
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414 Math Spring 2005 Homework Assignment 4 Due Thursday 24 February Section 9.3.7: 6, 7, 12, 13, 15, 17, 20; plus the problem below. 1. This problem completes the proof of the Stone-Weierstra Theorem given in class. Dene a sequence of polynonial functions {pn }n0 on [1, 1] by recursion as follows: = p0 0, x2 p2 (x) n pn+1 (x) = pn (x) + 2 for n 0. (a) Show that |x| pn+1 (x) = |x| pn (x) 1 |x| + pn (x) 2
for |x| 1. (b) Prove that 0 pn (x) pn+1 (x) |x| for |x| 1. (...
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