I'm trying to Plot this function:

enter image description here

Between the interval -0.2 < t < 0.1 but it doesn't work. All i get is a blank graph between my intervals. If you could help me out I'd greatly appreciate it.

This is my code:

Plot[Piecewise[{{Sqrt[t]*Sin[t^(-1)], x > 0}, {t*Sin[t^(-1)]}}], {t, -0.2, 0.1}]

closed as off-topic by xzczd, Bob Hanlon, m_goldberg, Henrik Schumacher, Lukas Lang Nov 4 '18 at 12:18

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – xzczd, Bob Hanlon, m_goldberg, Henrik Schumacher, Lukas Lang
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 1. The x should be t. 2. Syntax of Piecewise is wrong, please check the document of Piecewise for more information. The correct one should be Plot[Piecewise[{{Sqrt[t] Sin[1/t], t > 0}}, t Sin[1/t]], {t, -0.2, 0.1}] $\endgroup$ – xzczd Nov 3 '18 at 15:41
  • $\begingroup$ Oh my god. I've been spending way to much in front of the computer today it seems. I don't know what I was thinking when I put x instead of t. $\endgroup$ – wznd Nov 3 '18 at 15:46
  • $\begingroup$ No problem. These things happen to all of us. Anyways, since this is settled, I vote to close this post as "simple mistake". $\endgroup$ – Henrik Schumacher Nov 3 '18 at 20:56

Since the function is only defined at t == 0 in the limit and the Limit is 0, you want to specify both conditions in the Piecewise and let its default cover the limiting case.

Limit[Sqrt[t]*Sin[t^(-1)], t -> 0] == Limit[t*Sin[t^(-1)], t -> 0] == 0

(* True *)

    {Sqrt[t]*Sin[t^(-1)], t > 0},
    {t*Sin[t^(-1)], t < 0}}],
  {t, xmin, xmax},
  Frame -> True,
  FrameTicks -> All,
  WorkingPrecision -> 20,
  PlotPoints -> 200,
  MaxRecursion -> 10,
  PlotStyle -> AbsoluteThickness[0.5]],
 {{xmin, -0.2}, -0.2, -0.02, 0.02, Appearance -> "Labeled"},
 {{xmax, 0.1}, 0.02, 0.1, 0.01, Appearance -> "Labeled"},
 SynchronousUpdating -> False]

enter image description here


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