hw6 - MATH 410: Homework 6 Section 3.6 Due in class Friday...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 410: Homework 6 Section 3.6 Due in class Friday 3/9/2012 1. Define f : [0, ) R by f (x) = 1 + x2 . First prove that f fits the hypotheses for Theorem 3.29 in the book and then elaborate on what the consequence of this theorem is. Note: This is not a book problem. 2. Let D = [0, 1] (2, 3] and define f : D R by f (x) = x if 0 x 1 x - 1 if 2 < x 3 ** * Prove that f is continuous. Determine f -1 and prove that f -1 is not continuous. Does this contradict Theorem 3.29 in the book? Note: This is book problem 5. Section 3.7 1. Prove using sequences that: (a) lim (b) x1 x4 -1 x-1 = 4 1 lim x-1 = 2 x1 x-1 * * Note: This is book problem 2. 2. Suppose that f : R R has the property that there is some M > 0 such that |f (x)| M |x|2 for all x. Prove that f (x) =0 lim f (x) = 0 and lim x0 x0 x Note: This is book problem 9. ** ...
View Full Document

This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.

Ask a homework question - tutors are online