- #1
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Homework Help Overview
The discussion revolves around sketching the graph of a function, specifically focusing on the function's definition and periodicity. Participants are examining the constraints of the function's domain and the implications of extending the graph beyond its defined range.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants question the necessity of extending the function outside its defined interval of -l to +l. There are discussions about the correct interpretation of the problem statement and the periodic nature of the function, particularly regarding its period of 2l.
Discussion Status
Some participants have provided clarifications regarding the periodicity of the function and the correct expressions to use. There is an ongoing exploration of the implications of the problem statement, with no explicit consensus reached yet.
Contextual Notes
There is mention of a potential oversight in the problem statement that may affect the interpretation of the function's behavior. Additionally, participants are discussing the readability of the variable used in the function, indicating a focus on clarity in mathematical notation.
- #2
berkeman
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But your function looks to be only defined over -l to +l -- why are you asked to extend it outside of that definition? Is there more to the question? Is that really how the problem is stated in the book?
- #3
- #4
berkeman
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Ah, yes. You left out the "and" part...Setareh7796 said:
So the period of the waveform is 2l, right? So f(x) should equal f(2l), not f(3l/2)...
- #5
Mark44
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According to the belated problem statement, f(x) = f(x + 2l).berkeman said:
- #6
berkeman
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Yeah, thanks Mark. I meant f(x) = f(x + 2l), not = f(x + 3l/2). Trying to type too fast I guess...Mark44 said:
- #7
SammyS
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That " l ", lower case L, sure makes these expressions difficult to read. There is a Unicode character that will help, Unicode character U + 2113, which is rendered as ℓ .
f(x) = f(x + 2l) becomes f(x) = f(x + 2ℓ)
##\LaTeX##, can also give a good result. Its standard use of a serif font in italics for variables gives ##f(x) = f(x + 2l) ##.
But the script lowercase L can be displayed in ##\LaTeX##. Use "\ell" to get ##f(x) = f(x + 2\ell) ##.
Now I must say that "\ell" looks better written with ##\LaTeX## as \##ell##.
f(x) = f(x + 2l) becomes f(x) = f(x + 2ℓ)
##\LaTeX##, can also give a good result. Its standard use of a serif font in italics for variables gives ##f(x) = f(x + 2l) ##.
But the script lowercase L can be displayed in ##\LaTeX##. Use "\ell" to get ##f(x) = f(x + 2\ell) ##.
Now I must say that "\ell" looks better written with ##\LaTeX## as \##ell##.
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