Re: variables versus functions
- To: mathgroup at smc.vnet.net
- Subject: [mg28806] Re: [mg28797] variables versus functions
- From: BobHanlon at aol.com
- Date: Mon, 14 May 2001 01:32:58 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Clear[a, b, x, af, bf];
a = Cos[x];
b = ArcTan[x];
af[x_] := Cos[x];
bf[x_] := ArcTan[x];
Plot[a, {x, 0, 2Pi}];
FindRoot[a == b, {x, Pi/2}] ==
FindRoot[af[x] == bf[x], {x, Pi/2}]
True
However, if x has a definition prior to defining the variables
x = Pi/4;
a = Cos[x];
b = ArcTan[x];
{a, b}
{1/Sqrt[2], ArcTan[Pi/4]}
Plot[a, {x, 0, 2Pi}];
FindRoot[a == b, {x, Pi/2}]
\!\(\*FormBox[
RowBox[{\(FindRoot::"jsing"\), \(\(:\)\(\ \)\), "\<\"Encountered a singular
\
Jacobian at the point \\!\\(TraditionalForm\\`x\\) = \
\\!\\(TraditionalForm\\`1.5707963267948966`\\). Try perturbing the initial \
point(s).\"\>"}], TraditionalForm]\)
FindRoot[a == b, {x, Pi/2}]
Bob Hanlon
In a message dated 2001/5/13 3:34:17 AM, jsweet at engineering.ucsb.edu writes:
>How is it different to define a variable such as A=Cos[x]
>versus a function A[x_]:=Cos[x] ?
>
>Furthermore, what If I define two functions A[x_]:=Cos[x] and
>B[x_]=ArcTan[x]? How would FindRoot[A==B,{x,pi/2}] treat this
>differently than if I just used variable definitions for A & B?
>