Math 242: Principles of Analysis Fall 2016 Exam 3 Information . Department of Mathematics and Computer Science College of the Holy Cross

General Information

Important Definitions/Theorems/Axioms

• I will expect you to know how to use all of the definitions and theorems below to prove results similar to those on the homework assignments. You should know precise statements of the definitions and theorems in bold.
• Definition 3.1.1
• Theorem 3.2.3
• Theorem 3.2.4
• Theorem 3.2.8
• Theorem 3.2.9 (Squeeze Theorem)
• Definition 3.3.2
• Theorem 3.3.4
• Definition 3.4.1
• Theorem 3.4.10
• Theorem 3.4.11
• Theorem 3.4.13
• Theorem 3.4.16
• Theorem 3.5.2 (Intermediate Value Theorem)
• Definition 3.5.7
• Theorem 3.5.9
• Theorem 3.5.10 (Extreme Value Theorem)
• Definition 3.6.1
• Theorem 3.6.8
• Definition 4.1.1
• Theorem 4.1.8
• Theorem 4.2.1
• Theorem 4.2.5
• Theorem 4.3.3
• Theorem 4.3.9 (Rolle's Theorem)
• Theorem 4.3.11 (Mean Value Theorem)
• Definition 4.3.14
• Theorem 4.3.15
• Finally, I will ask you to write a complete proof of one of the following:
  • Theorem 3.2.3
  • Theorem 3.5.2
  • Theorem 3.5.9
  • Theorem 3.5.10
  • Theorem 4.3.9 and Theorem 4.3.11

Practice Questions