This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (A) 1. 1.1 # 4g 2. 1.1 # 4h 3. Prove for all n N that n i =0 (4 i + 3) = (2 n + 3)( n + 1). 4. (a) State Rolles Theorem from dierential Calculus. (b) Let a and b be real numbers. Prove for all n N that if f : R R is continuous on the interval [ a,b ], dierentiable on the interval ( a,b ), and has n roots in the interval [ a,b ], then the derivative f has at least n1 roots in the interval [ a,b ]. (B) 1. 1.1 # 11 (dont forget to prove uniqueness) 2. 1.1 # 17 3. Challenge problem: 1.1 # 18 (If you follow the hint, are you inducting on k or on n ?) Additional practice problems: 1.1 # 3, 4abcdehij, 5, 7 These problems will not be collected, but cover material that you will be responsible for knowing. 1...
View
Full
Document
This note was uploaded on 02/20/2012 for the course MATH 4000 taught by Professor Staff during the Spring '08 term at University of Georgia Athens.
 Spring '08
 Staff
 Algebra, Geometry

Click to edit the document details