Mathematica Why Is Mathematica Not Graphing This 3d Graph Correctly?

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The discussion centers on issues with graphing the function y = 5sin(1/x) in 3D using Mathematica, where the 3D representation does not match expectations. Users suggest that increasing the number of plot points is essential to avoid aliasing, as the function's high frequency near x = ±0.05 complicates accurate visualization. It is noted that the 3D graph is not correctly representing y = 5sin(1/x) but rather a function f(x,y) that includes y values outside the original equation. Recommendations include using the Plot3D function with a high number of plot points and adjusting MaxRecursion for better results. The documentation for Mathematica is criticized for being unclear, leaving users uncertain about proper implementation.
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Trying to graph y = 5sin(1/x) in both an 2d and 3d graph, and the 3d isn't looking right
As you can see from the image here, when I graph the 2d graph of y = 5sin(1/x), it comes out like I'd expect. However, when I graph it in a 3d graph, it doesn't look right at all. Can someone tell me why it isn't displaying right, or is it and I'm just missing something when I add the z axis?

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You need to increase the number of plot points. But this function is just an ugly function, so don’t get your hopes up.
 
I have no explanation for that 3D graph. Its behavior near ##x=\pm 0.05## (##1/x \approx 20## radians) is strange. In the 3D plot, it is not graphing ##y=5\sin(1/x)##. It is graphing ##f(x,y)=5\sin(1/x)##, where ##y\in [-6,6]## doesn't even appear in the equation.
 
As @Dale mentioned, this is a case of low sampling relative to the frequency of the function. It is known as aliasing.
 
Dale said:
You need to increase the number of plot points. But this function is just an ugly function, so don’t get your hopes up.
Thank you. How do I go about doing that in Mathematica? I'm thinking I probably need to actually learn the Mathematica language to have more versatility like that?
 
I don't have experience with Mathematica and do not have it to test things on, but this looks like something to try:
Plot3D[ ... as before ...., PlotPoints ->{10000, 3}]
Click the PlotPoints option documentation here.
You might also try adding MaxRecursion -> r. That is supposed to help when the function changes rapidly.
PS. This looks like TERRIBLE documentation, leaving a lot to guess about. Am I missing something?
 

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