# Warnings when plotting in ContourPlot a function defined as the solution of FindRoot

I am trying to plot implicitly a transcendental equation where one of the parameters (lambda) is given by another transcendental equation which, in this case, I can solve. Therefore, I defined lambda as

\[Lambda][St_, Le_, \[Rho]_, cp_, k_, \[Kappa]_, ms_, ml_, Di_, \[Alpha]_] :=
x /. FindRoot[(cl\[Infinity] F[-x/Sqrt[Di]] - cs\[Infinity] F[x])/
(F[-x/Sqrt[Di]] - F[x] ((1 - \[Alpha]) F[-x/Sqrt[Di]] + \[Alpha])) +
ml (\[Rho] F[x/Sqrt[Le]] (cp St Ts\[Infinity] - F[-x/Sqrt[Le \[Kappa]]]) -
St Tl\[Infinity] F[-x/Sqrt[\[Kappa] Le]])/(St (cp \[Rho] F[x/Sqrt[Le]] -
F[-x/Sqrt[\[Kappa] Le]])), {x, 1}]


where F[x] is a function that I have defined. Then, I define a quite convoluted function (called marg) where lambda appears several times. As I want to plot the curve where marg=0 varying two of the parameters, I use

ContourPlot[marg[St, Le, \[Rho], cp, k, \[Kappa], ms, ml, Di, \[Alpha]] == 0, {k, 0, 10}, {\[Kappa], 0, 10}, FrameLabel -> {"k", "\[Kappa]"}, PerformanceGoal -> "Quality"]


Everything worked perfectly but suddenly I started getting a lot of warnings (even though I still obtain the plots and they haven't changed from the ones I got without warnings). Some of the warnings are the following

• FindRoot::nlnum
• ReplaceAll::reps
• FindRoot::cvmit

I attach a screenshot with all the warning messages in case it helps.

How can I sort it out? Thank you very much in advance!

• you should define lambda and marg so they only take numeric arguments. ( do k_?NumericQ in the arg lists ) . Be sure to clear old function defs when you do that ) – george2079 Nov 22 '16 at 19:07
• It worked, thank you very much! – Ferran Brosa Planella Nov 23 '16 at 12:47