hw7additional-555-2011

hw7additional-555-2011 - f ) to evaluate the following...

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

View Full Document Right Arrow Icon
Extra problems Homework 7. (1) Let f : [0 , 1 R be a continuous function. Prove that lim n →∞ 1 n n X k =1 f ( k/n ) = Z 1 0 f ( x ) dx. (Hint: Use uniform continuity to show that for ± > 0 there exists a δ > 0 such that S ( σ ) - s ( σ ) < δ for all subdivisions σ with norm N ( σ ) < δ .) (2) Use the previous problem (by picking the right 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 ) to evaluate the following sums, where you can use calculus to evaluate the integral on the right. (a) lim n 1 n 3 n X k =1 k 2 (b) lim n n X k =1 n n 2 + k 2 . 1...
View Full Document

Ask a homework question - tutors are online