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Ast = plot(f,a/t,b/t,fill=True,color='blue',fillcolor=fillcolor,fillalpha=fillalpha,xmin=0,ymax=2.5) T = text("f(x) = {:.3f}/({:.3f} x)".format(float(s),float(t)),(2,2), fontsize='large') T += text("A(1,6) = A(1,3) + A(3,6)", (4,1.2), fontsize='x-large') if t == 3 and s == 3: T += text("A(1,3) + A(1,2)", (4.665,.9), fontsize='x-large') return Cst + Ast + T areas1 = ,alpha=.4,color='black')+line(,alpha=.4,color='black') for t in list(sxrange(1,3,.162841))+] areas2 = ] M = animate(areas1+areas2+10*]) M.save('log.gif')
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f(x)=1/x C = plot(f,.4,7,color='black', xmin=0, figsize=6.5) A2 = plot(f,1,3,fill=True,color='black',fillcolor=hue(.3),figsize=6.5) o = point((0,0), size=.00001) B = C+A2+o def A(s,t,a,b,fillcolor=hue(.6),fillalpha=.5): f(x) = s/(t*x) Cst = plot(f,.4/t,7/t,color='blue', xmin=0,ymax=2.5)
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An elementary proof that the area under 1/x satisfies the logarithm rule.
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