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Dragoni, Federica
Publisher: Cardiff University
Languages: English
Types: Other
Subjects: QA
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 2 Continuity. 23 2.1 Cluster points. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 De nitions of limits at a point. . . . . . . . . . . . . . . . . . 26 2.3 Theorems for limits. . . . . . . . . . . . . . . . . . . . . . . . 30 2.4 One-sided limits. . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5 Continuous functions. . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Algebra of continuous functions. . . . . . . . . . . . . . . . . . 39 2.7 The Intermediate Value Theorem . . . . . . . . . . . . . . . . 41 2.8 The Weierstrass Extreme Value Theorem. . . . . . . . . . . . 44
    • 3 Di erentiability and derivatives. 47 3.1 De nition and examples. . . . . . . . . . . . . . . . . . . . . . 47 3.2 Rules of di erentiation. . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Stationary points, local maximum and minimum points. . . . 56 3.4 Theorems for di erentiable functions. . . . . . . . . . . . . . . 59 3.5 Monotone functions. . . . . . . . . . . . . . . . . . . . . . . . 62 3.6 Further properties of maximum points and minimum points. . 64
    • 4 Higher order derivatives. 69 4.1 De nitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 1.
    • 1) f((nn 1)(1x)0!) (x
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