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Are you looking for this? ParametricPlot3D[{(1 + Cos[16 t]) Cos[t], (1 + Cos[16 t]) Sin[t], 1 + Cos[16 t]}, {t, 0, 2 Pi}] or perhaps you want something dynamical? Manipulate[ ParametricPlot3D[{(1 …

$Version "13.0.0 for Mac OS X ARM (64-bit) (December 3, 2021)" f[x_] := x^3; parplot1 = ParametricPlot[{x, f[x]}, {x, 0, 10}, PlotRange -> {{0, 10}, {0, 50}}, ImageSize -> 200, AspectRat …

To understand what you did wrong observe the differences in the colors between your code and mine. What do you see for the Sqrt function? Something is different. Something is also different for the va …

You can use Exclusions ContourPlot[l^2*Sin[a]^2 - Sin[l*a]^2 == 0, {a, 0, 2*Pi}, {l, 0, 5}, PlotPoints -> 500, Exclusions -> {l == 1}] Edit: addressing the comment. This is not elegan, it's a ve …

Another way was suggested by @kglr and it works in the following manner: PolarPlot[ 0.5 (7.89 + 8.12 Cos[4 t] + 8.526 (Sin[4 t])^2), {t, Pi/4, 3 Pi/4}] /. xx_Line :> {xx, Dynamic[Lighter@Light …

ContourPlot[((Pi Q^2 + Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])/8 + (2 J^2)/( l^2 (Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])) - Pi/4 Q^2 Log[l/8 (Pi Q^2 + Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])] /. l -> 1) == 2, { …

If you want a to be an arbitrary parameter you can try to use Manipulate Manipulate[ Plot[2*(a^2 - x^2) - ((a^2 + x^2))^2, {x, -10, 10}], {a, -10, 5}]

There's a mistake with the brackets. The following works fine f[x_] = Sin[x] g[x_] = Cos[x] Plot[{Sin[x], Cos[x]}, {x, -2*Pi, 2*Pi}, PlotStyle -> {{Black}, {Blue}}]

g = 1; dm = DynamicModule[{a}, Column[{Dynamic@ Plot[Sin[(a + g) x], {x, 0, Pi}, PlotRange -> {All, {-1, 1}}], Slider[Dynamic@a, {0, 4}]}]]; Button["g++", g = g + 1] Dynamic[dm] Ed …

Edit: as per the request the following encodes all the requirements Labeled[ ListPlot[ RandomReal[10, 100], ImageSize -> Large, Frame -> True, FrameLabel -> { {Column[{Style["Column1", Fo …

Edit 2 pl = Plot[Sin[x], {x, 0, 2 Pi}, PlotStyle -> { Red, Thickness[0.03] } ][[1]]; Plot[Sin[x], {x, 0, 2 Pi}, PlotStyle -> None, Frame -> True, FrameTicksStyle -> Dire …

Edit: addressing the comment ContourPlot[ Evaluate@{eqs}, {x, -ax - 1, ax + 1}, {y, -bx - 0.5, bx + 0.5}, Epilog -> { Red, PointSize[0.02], Point[gpts], Black, Text[Framed[Column[{g …

Maybe I am missing something, but I don't see what. Anyway, with a minimal amendment of the code in the OP we have: f[x_] := Log[1 + x] + x E^-x g[x_] := D[f[x], x] // FullSimplify point = {0, f[0]} p …

Is the following sufficient? If yes, then you want to have a look at ToRadicals forplot = ToRadicals[{x^(-1), x^0, Root[#^3 - x &, 1], x^(1/2), Root[#^3 - x^2 &, 1], Root[#^8 - x^7 &, 2], x, x …

This is not the best answer, but perhaps a good starting point. There exists a resource function developed by @Carl Woll that is called GraphicsInformation You can do "ImageSize" /. ResourceFunction[" …