Questions: Fill in each blank so that the resulting statement is true. If there exists a positive number p such that f(t+p)=f(t), function f is . The smallest positive number p for which f(t+p)=f(t) is called the of f.

Fill in each blank so that the resulting statement is true. If there exists a positive number p such that f(t+p)=f(t), function f is . The smallest positive number p for which f(t+p)=f(t) is called the of f.

Transcript text: Fill in each blank so that the resulting statement is true. If there exists a positive number $p$ such that $f(t+p)=f(t)$, function $f$ is $\qquad$ .The smallest positive number $p$ for which $f(t+p)=f(t)$ is called the $\qquad$ of f .

Solution

Solution Steps

Step 1: Identify the property of the function

The statement describes a function \( f \) that repeats its values at regular intervals. This property is known as periodicity.

Step 2: Define the period of the function

The smallest positive number \( p \) for which \( f(t+p) = f(t) \) holds true is called the period of the function \( f \).

Step 3: Fill in the blanks

The first blank should be filled with periodic.
The second blank should be filled with period.

Final Answer

periodic
period

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