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Lectures on differential calculus of functions of one variable
13. Continuity of a function on a set
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Table of contents
Preface
Video lectures
Preliminary information
1. Boundaries of sets
2. Limit of a sequence
3. Properties of the limit of a sequence
4. Infinite limits
5. Monotone sequences
6. Nested segments theorem and Bolzano-Cauchy theorem on the limit point
7. Subsequences. Cauchy criterion
8. The limit of a function
9. Properties of the limit of a function
10. One-sided limits. Some important function limits
11. The limits of monotone bounded functions
12. Continuity of function at a point
13. Continuity of a function on a set
14. Points of discontinuity
15. O-notation
16. Differentiable functions
17. Properties of differentiable functions
18. Hyperbolic and inverse hyperbolic functions
19. Physical sense and geometric sense of the derivative
20. Higher-order derivatives
21. The basic theorems of differential calculus
22. Taylor's formula
23. L'Hospital's rule
24. Application of differential calculus to the study of functions
References
Index
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