(*pomocniczadefinicja*)​​arrows[function_,x0_,n_]:=Module[​​{l=NestList[function,x0,n]},​​l=Prepend[Flatten[Transpose[{Transpose[{Most[l],Rest[l]}],Transpose[{Rest[l],Rest[l]}],Transpose[{Rest[l],0Rest[l]}]}],1],{l[[1]],0}];​​Arrow/@Transpose[{Most[l],Rest[l]}]​​]
In[]:=
(*zadanie1*)​​Sum[k(k-1),{k,2,n}]​​Sum[k^2,{k,1,n}]​​Sum[k^3,{k,1,n}]
Out[]=
1
3
(-1+n)n(1+n)
Out[]=
1
6
n(1+n)(1+2n)
Out[]=
1
4
2
n
2
(1+n)
In[]:=
(*zadanie2*)​​n=Range[40];​​ListStepPlot[{​​FoldList[Plus,1/n^2],​​2n/(n+1)​​}]
Out[]=
10
20
30
40
1.0
1.2
1.4
1.6
1.8
2.0
In[]:=
(*zadanie3*)​​n=Range[40];​​ListStepPlot[{​​Sqrt[n],​​FoldList[Plus,1/Sqrt[n]],​​2Sqrt[n]​​}]
Out[]=
10
20
30
40
2
4
6
8
10
12
(*zadanie8*)​​f=Function[x,(x^2+1)/4];​​Show[​​Plot[{f[x],x},{x,0,6},AspectRatioAutomatic,ImageSize800],​​Graphics[{Arrowheads[Small],Thickness[Large],Red,arrows[f,0,4],Purple,arrows[f,2,4],Brown,arrows[f,4,4]}]​​]
Out[]=
In[]:=
(*zadanie10*)​​f=Function[x,x^3+1/4x-1/4];​​Show[​​Plot[{f[x],x},{x,-2,2},AspectRatioAutomatic,PlotRange{-3,3},ImageSize800],​​Graphics[{Arrowheads[Small],Thickness[Large],Red,arrows[f,-.53,30],Purple,arrows[f,0.9,30],Brown,arrows[f,1.1,4]}]​​]
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