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? >