MATH 131b Intro To Rl Variab San Jose State

HOW DISCONTINUOUS CAN f BE? SLOBODAN N. SIMIC Let I be an interval and f : I R an everywhere dierentiable function. Darbouxs theorem states that f has the intermediate value property (IVP). Remember that this doesnt mean f is continuous, for there

San Jose State University Department of Mathematics Fall 2007 Math 213: Advanced Dierential Geometry Instructor: Slobodan Simic, simic@math.sjsu.edu, (408) 924-7485 Time: MW 13:30-14:45 (subject to change) Prerequisite: Math 113 or instructor c

MATH 131B, SPRING 2007 HOMEWORK 9 SOLUTIONS 1 Sec. 11.2, ex. 1: Let Un = (1 + n , 3), n 1. Then U = {Un } is an open cover of (1, 2]. We claim that U has no nite subcover. Suppose that it did and denote it by {Un1 , . . . , Unk }. Let n = max{n1 ,

San Jose State University Math 131B, Spring 2006 Sample Midterm Solutions 2 Name: XYZ Score 1 25 2 25 3 25 4 25 Total 100 Explain your work 1. (25 points) Suppose fn : [0, 1] R is a sequence of bounded functions which converges uniformly to f

San Jose State University Department of Mathematics Colloquium Series presents Alexander Givental UC Berkeley Keplers laws and conic sections April 25, 2007, MH 423 Abstract: Why are Keplers orbits conic sections? What is the cone whose sections

MATH 131B, SPRING 2007 HOMEWORK 2 SOLUTIONS Sec. 6.3, ex. 5: Note that 1 x2 sin x f (x) x 0 = . |x| g(x) sin x sin x Using the fact that x/ sin x = (sin x/x)1 1, as x 0, we obtain that the right-hand side goes to 0, as x 0. The Squeeze Theorem

San Jose State University Math 131B, Spring 2007 Midterm 1 Solutions February 26, 2007 Name: Erastus Hamm Score 1 25 2 25 3 25 4 25 Total 100 Explain your work 1. (25 points) Let f : R R be dened by f (x) = |x| sin x. (a) Show that f is diere

A campus of The California State University Office of the Academic Senate One Washington Square San Jose, California 95192-0024 408-924-2440 Fax: 408-924-2451 S04-12 At its meeting of May 17, 2004, the Academic Senate passed the following Policy

San Jose State University Math 131B, Spring 2006 Sample Midterm 2 Name: Score 1 2 3 4 Total Explain your work 1. (25 points) Suppose fn : [0, 1] R is a sequence of bounded functions which converges uniformly to f on [0, 1]. Prove that f1 (x) +