Re: Find many Roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg32103] Re: Find many Roots*From*: Tom Burton <tburton at cts.com>*Date*: Mon, 24 Dec 2001 23:44:34 -0500 (EST)*References*: <a06p90$fb1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hello, On Mon, 24 Dec 2001 08:33:36 +0000 (UTC), in comp.soft-sys.math.mathematica you wrote: >Tan[x]==1/x, {x,0,12}] For this particular problem, I would select: Step 1: Find the approximate roots visually: p1 = Plot[Tan[x]-1/x, {x,0,12}, PlotRange -> {-1,1}]; approx = {1, 3, 6, 10}; Step 2: Refine these approximations: answers = FindRoot[Tan[x] == 1/x, {x,#}] & /@ approx Step 3: Verify solutions (Tan[x] - 1/x) /. answers Step 4: Check for missing solutions Show[ p1, Graphics[{Hue[0], PointSize[0.03], Point[{x,0}] /. answers}] ] I higly recommend a visual method, but iff you need a more automated method, I would suggest something like answers = FindRoot[Tan[x] == 1/x, {x,#}] & /@ Range[1,12] xx = Select[ Union[ x /. answers, SameTest -> (Abs[#1-#2]<10^-6 &) ], 0 <= # <= 12 &] Tom Burton