
Title: Test Functions

Series: Distributions

YouTubeTitle: Distributions 2  Test Functions

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Quiz: Test your knowledge

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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: $$ \mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) = 0 } $$