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Hey, @Cyrille!

I found it useful to pass the taylor=True option to the limit (or lim) function:

U_5(x,a,b,γ) = ((1-γ)/γ)*(((a*x)/(1-γ))+b)^γ 
show(U_5(x, a, b, γ))
print('Computing')
limU = lim(U_5, γ=1, taylor=True)
print('Finished')
show(LatexExpr(r"\lim_{\gama\rigtharrow 1}U_5(x, a, b, γ) = "),limU)

I believe that this option must be used carefully, due to some known bugs in Maxima, but in this case it works like a charm!

Hope this helps!