The Function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 + 5 x & \text { if } x > 0\end{array} \right\}$

question 17

Multiple Choice

The function $f ( x ) = \left\{ \begin{array} { c c } x & \text { if } x < 0 \\2 + 5 x & \text { if } x > 0\end{array} \right\}$ has a Fourier series on $[ - 2,2 ]$ that converges at $x = 0$ to

• A) 0
• B) 1
• C) 1/2
• D) 2
• E) unknown

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Definitions:

Assumption

A belief or statement taken for granted without proof, often used as a starting point for further reasoning or argument.

Science

Employing rational thought to transition from noticeable, quantifiable data to conjectures and then to verifiable theories explaining those data.

Experimental Material

The group or class of objects or subjects that is being studied in an experiment.

Independent Variable

The variable in an experiment that is manipulated or changed by the researcher to observe its effects on the dependent variable.