# hw1 - , 1]: (i) f ( x ) = x 3 ; (ii) f (1 / 2) = 1 ,f ( x )...

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Math 128a, fall 2011, Chorin, theory homework 1, due in the week of Sept. 5. 1. Use the formula for the error in interpolation to show that if two polyno- mials P n ,Q n of degree n coincide at n +1 distinct points, then they are identical and coincide at all points. 2. Suppose you represent the function f ( x ) = e x in the interval [0 , 3] by the ﬁrst 7 terms of its Taylor series. Find a bound for the diﬀerence between f and the sum of these terms in that interval. 3. Find the maximum norm of the following functions on the interval [0
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Unformatted text preview: , 1]: (i) f ( x ) = x 3 ; (ii) f (1 / 2) = 1 ,f ( x ) = 0 when x 6 = 1 / 2. (iii) f ( x ) =-x 100 . 4. Find the least squares norm of each of the functions in the previous prob-lem. 5. Consider the function f ( x ) = x n , where n is a positive integer; ﬁnd its maximum norm and its least squares norm. Find what happens to these norms as n → ∞ . 1...
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## This note was uploaded on 01/21/2012 for the course MATH 128A taught by Professor Rieffel during the Fall '08 term at University of California, Berkeley.

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