08wHW3 - f which is improperly integrable on [0 , + ) and L...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MAT 125B Homework 3 M.Fukuda Please submit your answers at the discussion session on February 5 Tuesday. 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. i) Let I = (0 , 1] and f ( x ) = 1 /x p where p R . Find all p for which f is improperly intergrable in I . ii) By using i) show that the product of two improperly integrable functions is not neces- sarily improperly intergrable. iii) Find two functions where each function is not improperly integrable but the sum is improperly integrable. 2. i) Suppose we have a function
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online