       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, 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

```

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