Calculus I Lecture 10A Proof by Contradiction and Rolles Theorem
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#Calculus #USF #USFMath #GoBulls • Today: Proof by Contradiction and Rolle's Theorem • Overview of the Theorems in Module 3 (1:45) • Proofs by Contradiction (5:08) • ○ The Proof that the Square Root of Two is Irrational. (6:28) • Rolle's Theorem (11:16) • ○ Proof of Rolle's Theorem (12:20) • ○ An Example of Using Rolle's Theorem (17:29) • State Mean Value Theorem (20:42) • • In the Book: Suggested Problems • (Note, these are the problems for both 10A and 10B) • Section 4.2, Examples 2, 3, and 5. Problems 1, 3, 5, 7, 17, 19, 23, 24, 25 • = Chapters = • 0:00 Introduction • 1:43 Proofs of Module 3 Overview • 5:08 Proof by Contradiction • 6:28 sqrt(2) is Irrational • 11:16 Stating Rolle's Theorem • 12:20 Proof of Rolle's Theorem • 17:29 Example using Rolle's Theorem • 20:42 Stating Mean Value Theorem
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