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Can you prove it? The Intermediate Value Theorem
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Classroom Contents
Limits and Continuity
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- 1 Epsilon Delta Continuity (Example 1)
- 2 The Ultimate Continuity Battle (Example 2)
- 3 f is not continuous (Example 3)
- 4 Epsilon Delta Continuity (Example 4): x^3
- 5 Epsilon Delta Continuity (Example 5): Absolute Value
- 6 Epsilon Delta Continuity (Example 6): 1/x
- 7 Epsilon Delta Continuity (Example 7): Square Root
- 8 Sequential vs Epsilon-Delta Continuity
- 9 f+g is continuous
- 10 fg is continuous
- 11 f/g is continuous
- 12 Chen Lu is continuous
- 13 Max is continuous
- 14 The Popcorn Function
- 15 f(2x) = f(x)
- 16 f(x^2) = f(x)
- 17 Continuous implies Bounded
- 18 Can you prove it? The Extreme Value Theorem
- 19 Can you prove it? The Intermediate Value Theorem
- 20 Image of an interval
- 21 What is a fixed point?
- 22 Calculus Square Root
- 23 a pyramid fact about functions
- 24 Continuity and Monotonicity
- 25 f inverse is continuous
- 26 The Borsuk Ulam Theorem
- 27 What is Uniform Continuity?
- 28 Uniform Continuity (Example 1): The Basics
- 29 Uniform Continuity (Example 2): Challenging Example
- 30 Uniform Continuity (Example 3): Not Uniformly Continuous
- 31 Uniform Continuity (Example 4): Not Uniformly Continuous
- 32 Hölder Continuity
- 33 Uniform Continuity and Compactness
- 34 Voulez-vous Cauchy avec moi?
- 35 What is a continuous extension?
- 36 a neat fact about uniform continuity
- 37 The Darboux Integral
- 38 Epsilon delta limit (Example 1)
- 39 Epsilon delta limit (Example 2)
- 40 Epsilon delta limit (Example 3): Infinite limit at a point
- 41 Epsilon delta limit (Example 4): Limits at infinity
- 42 Epsilon delta limit (Example 5): x cubed
- 43 Epsilon delta limit (Example 6): Square Roots
- 44 Epsilon delta limit (Example 7): 1/x
- 45 How do you prove it? The Squeeze Theorem
