1+1

2+4

6+1
a+b

(Sqrt[5])

(25^(1/4))

(Sqrt[5.])

N[(Sqrt[5])]

N[(Sqrt[5]),20]

?Sin

(a+1)-(b-c)
((a+1)-(b-c))*(a/3)

MatrixForm[{{2,4},{5,13}}]

ClearAll[a,b,soucet](*tohle je komentar*)
a=5;
b=7;
soucet=a+b
2*soucet
soucet1

a=3

ClearAll[a]

Sin[Pi/3]
N[Sin[Pi/3],50]

LaplaceTransform[(E^(t+2))*(t^4)+Sin[2*t+0.4],t,s]

e;
E;
N[E];
E//N;
N@E;

100!//N

Plot[(t^4)*Cos[5*t+1]-3,{t,0,3Pi}]

DSolve[{(x^3)*y''[x]+(x-1)*y'[x]+2*y[x]==0,y[1]==2,y'[1]==1},y[x],x]

(*2.cviceni*)

mujlist={1,2,{auto,pocitac,{hop,skok}},Praha,Brno};
mujlist[[1]]
mujlist[[3]]
mujlist//TreeForm

mujlist[[3,1]]
mujlist[[3]][[1]]

mujlist//Length

mujlist[[-1]]

mujlist[[6]]

mujlist[[0]]

xylist={y,x,y,y,x,x,x,y}

xylist/.x->3

prirazeni={a->1,b->3,x->10,z->-2}

xylist/.prirazeni

xylist/.{x->1,x->3}
xylist/.{x->s,s->5}
(*xylist//.{x->s,s->5}
xylist//.{x->s,s->x}*)(*pro zajimavost*)

rce=(x^4)+((x^2)/(k^2))+k*x+(2/3)==0;
res=Solve[rce,x];
x1=x/.res[[1]];
x2=x/.res[[2]];
x3=x/.res[[3]];
x4=x/.res[[4]];
soucet=Abs[x1]+Abs[x2]+Abs[x3]-Abs[x4];
Plot[soucet,{k,-5,5},PlotStyle-> {Orange,Thick,DotDashed},AxesLabel->{"k","f(k)"},GridLines-> Automatic]

res=Solve[{2(x^2)-(y^2)-(3/5)==4k,y-(x^2)==k},{x,y}];
xka=x/.res;
Plot[xka,{k,-15,1},PlotStyle-> {{Blue,Thick},{Red,Thick},{Black,Thick,Dashed},{Brown,Thick,Dashed}},GridLines-> Automatic, AxesLabel-> {"k","f(k)"}]

xka

ClearAll[f,g]
f[x_]:=(x/3)*Tanh[2x+1]
g[psi_]:=((Sin[psi]+psi)/(Cos[psi]-(psi^2)))
Plot[g[6*f[((Sqrt[t+1])/t)]],{t,1,9},PlotStyle-> {Green,Thick,Dashed},GridLines-> Automatic,AxesLabel-> {"t","g(6*f(((Sqrt[t - 1])/t)))"}]

(*Treti cviceni*)

res=x/.Solve[((x*t)/5)+(((2*t*x))^2)-((4(x^3))/((t^3)-3))==Tanh[(t^2)],x][[1]];
f[t_]=((Abs[res[[1]]]-Abs[res[[2]]])/(1-Abs[res[[3]]]));
Plot[f[(1/3)*(Sin[2*x]+Cos[(x/2)])],{x,-20,20},PlotStyle-> {Green,Thick},GridLines-> Automatic,AxesLabel-> {"x","f(x)"}]

res=Solve[((x*t)/5)+(((2*t*x))^2)-((4(x^3))/((t^3)-3))==Tanh[(t^2)],x];
Length[%];
x1=x/.res[[1]];
x/.res[[1]];

Solve[Sin[x]==x,x]

FindRoot[Sin[x]==x,{x,20}]

Solve[Sin[x]==0,x]

FindRoot[Sin[x]==0,{x,2}]

FindRoot[Sin[x]==0,{x,(Pi/2)}]

ClearAll[f,g]
f[fce_,x0_]:=fce'[x0]*(x-x0)+fce[x0];
g[t_]:=(t^3)-3(t^2);
Plot[{f[g,1],g[x]},{x,-1,3},PlotStyle-> {{Blue,Dashed},{Red,Thick}},GridLines-> Automatic,AxesLabel-> {"x","f(x)"},Epilog->{PointSize[Medium],Point[{1,g[1]}]},PlotRange-> {Automatic,{-6,2}}]

Manipulate[
Plot[{f[g,Man],g[x]},{x,-1,3},PlotStyle-> {{Blue,Dashed},{Red,Thick}},GridLines-> Automatic,AxesLabel-> {"x","f(x)"},Epilog->{PointSize[Medium],Point[{Man,g[Man]}]},PlotRange-> {Automatic,{-6,2}}] ,{Man,-1,3}
]

rada=Table[{i,(Sqrt[i])},{i,0,10,1}];

list={2,5,8,9,12};
ListPlot[list];

body=ListPlot[rada(*,Joined->True*)];
proklad=Fit[rada,{1,(Sqrt[x])},x]
Show[body,Plot[proklad,{x,0,10}]]

SeedRandom[1]
radaNova=Table[{i,(Sqrt[i])+Random[]},{i,0,10,.1}];

bodyNova=ListPlot[radaNova,PlotStyle->{PointSize[.01],Green}];
prokladNova=Fit[radaNova,{1,(Sqrt[x]),x},x];
graf=Plot[prokladNova,{x,0,10},PlotStyle->Red];
Show[bodyNova,graf]

bodyNova=ListPlot[radaNova];
prokladNova=Fit[radaNova,Table[(x^i),{i,0,4,1}],x];
graf=Plot[prokladNova,{x,0,10},PlotStyle->Red];
Show[bodyNova,graf]