• Title: Test Functions

• Series: Distributions

• YouTube-Title: Distributions 2 | Test Functions

• Bright video: https://youtu.be/500gENxWiSU

• Dark video: https://youtu.be/qtcqQxVzBZs

• Subtitle on GitHub: dt02_sub_eng.srt missing

• Timestamps (n/a)
• Subtitle in English (n/a)
• 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: $$\mathrm{supp}(f) = { x \in \mathbb{R}^n \mid f(x) = 0 }$$

• Back to overview page