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

    Examples and counter-examples in analysis

    作者:Vincent Pantaloni
    主題:函數, 函數圖形, 極限值, 分段函數, 冪函數, Sequences and Series, 三角函數
    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

    下一步
    Boundedness is not preserved by pointwise convergence.

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