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Title: Test Functions
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Series: Distributions
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YouTube-Title: Distributions 2 | Test Functions
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Bright video: https://youtu.be/500gENxWiSU
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Dark video: https://youtu.be/qtcqQxVzBZs
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: dt02_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What does the notation $C_c^\infty( \mathbb{R}^n)$ mean?
A1: The set of all differentiable functions.
A2: The set of all functions that are arbitrarily often differentiable and have compact support.
A3: The set of all functions that are arbitrarily often differentiable and that have value 0 at the origin.
A4: The set of all continuous functions with compact support.
Q2: How many elements does the set $C_c^\infty( \mathbb{R}^n)$ have?
A1: Only one, the zero function.
A2: Infinitely many.
Q3: What is the correct definition for the support of a function $f$?
A1: $$ \mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) \neq 0 } $$
A2: $$ \mathrm{supp}(f) = \overline{{ x \in \mathbb{R}^n \mid f(x) \neq 0 }} $$
A3: $$ \mathrm{supp}(f) = \overline{{ x \in \mathbb{R}^n \mid f(x) = 0 }} $$
A4: $$ \mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) = 0 } $$
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Last update: 2024-11