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Theorems of Differential Calculus
- The Theorems of Differential Calculus
- Mean Value Theorem: Quick Intuitive Tests
- Hypotheses of the Theorems of Calc 1
- Finding a tricky limit two ways
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Theorems of Differential Calculus
Charlie Barnes, Oct 16, 2020
Includes:
- The Squeeze Theorem
- The Intermediate Value Theorem
- The Extreme Value Theorem
- The Mean ValueTheorem
- L'Hopital's Rule
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1. The Theorems of Differential Calculus
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2. Mean Value Theorem: Quick Intuitive Tests
-
3. Hypotheses of the Theorems of Calc 1
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4. Finding a tricky limit two ways
The Theorems of Differential Calculus
Below are statements of theorems from differential calculus with accompanying visualizations.
The Squeeze Theorem
If:
- , , and are all continuous functions over ,
- ,
- is between and on , and
- ,
The Intermediate Value Theorem
If:
- is continuous over and
- is a number between and
The Extreme Value Theorem
If:
- is continuous over ,
The Mean Value Theorem
If:
- is continuous over and
- is differentiable over ,
L'Hopital's Rule
If:
- and are both differentiable near ,
- or , and
- exists,
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