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Unformatted text preview: MAT 125A Homework 3
M.Fukuda
Please submit your answers at the discussion session on October 25th Thursday. You can use theorems in the lecuture unless otherwise stated. When you do so write those statements clearly instead of quoting them by numbers. 1. Let s, t R and f1 , f2 : (s, t) R. Take a (s, t) and, suppose limxa f1 (x) and limxa f2 (x) exist. Let Li = limxa fi (x) for i = 1, 2. 1) Suppose L1 , L2 R. Then, show that L = limxa f1 (x)+f2 (x) exits and L = L1 +L2 . 2) Suppose L1 R and L2 = . Then, does the limit L = limxa f1 (x) + f2 (x) exist? Prove your idea. 3) Suppose L1 =  and L2 = . Then, does the limit L = limxa f1 (x) + f2 (x) exist? Explain your idea briefly. 2. Find the redious of convergence and determine the exact interval of convergence. i)
n x n n ; ii)
n n3 3n xn ; iii)
n 1 (n + 1)2 2n xn ; iv)
n (1)n n2 4n xn 3. Let fn (x) = x/n on [0, ). i) Find f (x) = lim fn (x). ii) Determine if fn f uniformly on [0, 1] and prove your idea. iii) Determine if fn f uniformly on [0, +) and prove your idea. 1 ...
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This note was uploaded on 04/08/2008 for the course MATH 125A taught by Professor Fukuda during the Fall '07 term at UC Davis.
 Fall '07
 Fukuda

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