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This plot is Indeterminate at x==0:

siney = Plot[Sin[x]/x, {x, -5 \[Pi], 5 \[Pi]}, 
  PlotRange -> {{- 5 \[Pi], 5 \[Pi]}, {-1, 1}}, Frame -> True, 
  Exclusions -> x == 0, ExclusionsStyle -> Red]

So why an I not getting a red vertical at that point?

cybervigilante
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  • Limit[Sin[x]/x, x -> 0] gives 1. Could you please draw what graphical output you are expecting? – Syed Nov 11 '22 at 23:07
  • It is there, it is just too small to see easily. Use Plot[Sin[x]/x, {x, -5 Pi, 5 Pi}, PlotRange -> {{-5 Pi, 5 Pi}, {-1, 1.1}}, Frame -> True, Exclusions -> x == 0, ExclusionsStyle -> Directive[Red, AbsoluteThickness[4]]] – Bob Hanlon Nov 11 '22 at 23:10
  • @Syed - Done. Thanks. – Bob Hanlon Nov 11 '22 at 23:15
  • If you use Sinc[x] the exclusion isn't necessary. – Bob Hanlon Nov 11 '22 at 23:17
  • Ah, making it thicker worked. I was also expecting a line as in a tangent exclusion, but of course the y value at x==0 is finite and visible. Sinc is also handy, being a predefined function. – cybervigilante Nov 12 '22 at 07:23

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