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  1. Examples and counter-examples in analysis
    1. Pointwise convergence

    Examples and counter-examples in analysis

    Autor:Vincent Pantaloni
    Tópico:Continuidade, Funções, Gráfico de função, Limites, Funções Potência, Sequências e séries, Funções trigonométricas
    Animations to illustrate lessons in analysis

    Pointwise convergence

    Some animations to illustrate what pointwise convergence is and some counter-examples regarding this notion.

    • Boundedness is not preserved by pointwise convergence.

    • Continuity is not preserved by pointwise convergence.

    • Differentiability is not preserved by pointwise convergence.

    • fn converges does not imply f'n converges

    • Integration counter-examples : Witch's hat functions

    • Integration and uniform convergence

    Próximo
    Boundedness is not preserved by pointwise convergence.

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