problems with ReplaceAll

Questions
1

Hi everybody!

When I was trying to compile the following code, a very strange mistake occured (in some cases there was nothing to be shown and in other cases - the code began evaluating and then unexpectedly stopped). In what way might that code be improved or corrected?

Thanks a lot in advance. 

<code>
Manipulate[
f[x_] := Sin[t*x];
g[x_] := Cos[u*x];
Plot[Evaluate[(f[x] + g[x])] /. {t -> (s/2), u -> 8*v}, {x, 0,
8*Pi}], {s, 0, 20}, {v, 0, 6}];
</code>
2

On my system it seems to work as expected if only I remove the “;” character at the very end.

3

The semicolon suppresses output.

If you evaluate “2+2”, Mathematica will give “4”. If you evaluate “2+2;”, Mathematica will give nothing as output.

4

I think you also want to add a TrackedSymbols option so that the Manipulate does not continually eat up cpu cycles:

Manipulate[f[x_] := Sin[t*x];
 g[x_] := Cos[u*x];
 Plot[Evaluate[(f[x] + g[x])] /. {t -> (s/2), u -> 8*v}, {x, 0, 
   8*Pi}], {s, 0, 20}, {v, 0, 6}, TrackedSymbols :> {s, v}]
5

TrackedSymbols works well here as Jim points out. An alternative is to specify your function definitions in the Initialization option as in

Manipulate[
 Plot[Evaluate[(f[x] + g[x]) /. {t -> (s/2), u -> 8*v}], {x, 0, 8*Pi}],
 {s, 0, 20}, {v, 0, 6},
 Initialization ->
  {f[x_] := Sin[t*x],
   g[x_] := Cos[u*x]}]

Note also that I put the replacement rule inside the Evaluate as this is more in line with what Evaluate’s intended use is here.