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Unformatted text preview: f which is improperly integrable on [0 , + ) and L = lim x + f ( x ) exists. Then, show that L = 0. ii) Let f ( x ) = 1 n x < n + 2 n , n N otherwise . Then, show that f is improperly integrable on [0 , + ) but lim x f ( x ) does not exists. 3. i) Let d ( x, y ) = b x y b for x, y R . Show that d ( , ) satises the conditions of distance. ii) Let T : R n R m and b b be the Euclidean norm dend in R n and R n . Prove that sup b x b =1 b T ( x ) b = sup b x bn =0 b T ( x ) b b x b . 1...
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This homework help was uploaded on 04/08/2008 for the course MATH 125B taught by Professor Fukuda during the Winter '07 term at UC Davis.
- Winter '07