1+1

BaseForm[2,2]

PrimePi[2]

Sin[3]

sin[3]

(Sqrt[2])

(Sqrt[2.])

46.*(Sqrt[2])

N[(Sqrt[2])]

N[(Sqrt[2]),50]

N[(Sqrt[3])]

Solve

(Sqrt[\[Placeholder]])

(2^3)

(a/(b
((a+b)/(c+d
))))

∫(E^x)*Sin[x]*Cos[x]*x\[DifferentialD]x

fel=3

fel

Clear[fel]

Clear[Sin]

I=5

∫(E^x)*Sin[x]*Cos[x]*x\[DifferentialD]x

Plot[(1/50) (E^x) ((4-10 x) Cos[2 x]+(3+5 x) Sin[2 x]),{x,-18.42477796076938`,18.42477796076938`}]

A=5;
B=2;

Solve[A*x+B==10,x]

A=5;
B=N[2];

Solve[A*x+B==10,x]

(((a+b)*(c+9d))/(3*(2+(1+x*(3+1)))))

{A,B}

TreeForm[{1,3,2,4,5,{2,5,4,8}}]

Solve[{2*x+y==2,3*x-6==y},{x,y}]

Solve[{2*x+y==2,3*x-6==y},{x,y}]

Clear[x]
Solve[x==2,x]

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

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

2 3

10vez

vez10=25

vez10

N[Pi]
N[E]
N[Log[3]]

cosfi=0.4;

fi=ArcCos[cosfi];
Sin[fi]

N[(Sqrt[2])]

(Sqrt[2])//N

N@(Sqrt[2])

(*zde zacina druhe cviceni 29.2.2016*)

Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}]

Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}]

Plot[(-4-(Sqrt[2]) √(-132-1293 c+1065 (c^2)-50 (c^3)))/(2 (-7+5 c)),{c,-5,5}]

{1,2,3,5,{1,8,4},1}[[5,2]]

res=Solve[{(x^2)+x*y+c==20,y+10*y*c+15*x==8},{x,y}];

res[[3]]

x/.{x->1}

y/.{x->1}

Solve[(x^2)+3*x+1==0,x]

x/.{x->1,x->2}[[2]]

x+y/.{x->1,y->2}

x

x1=x/.res[[1]];(* koren x1*)
x2=x/.res[[2]];(* koren x2*)
y1=y/.res[[1]];(* koren y1*)
y2=y/.res[[2]];(* koren y2*)

z=3
Plot[{x1,x2,y1,y2},{c,-5,5},PlotStyle->{{Red,Thick,DotDashed},{Green,Dashed,Thick},Hue[0.6],RGBColor[0.7,0.15,0.6]},AxesLabel->{"c","x1,x2,y1,y2"},PlotLegends->{"x1","x2","y1","y2"},PlotRange->{Automatic,{-5,10}},PlotLabel->"Graf 1"]

Plot[2*(x^2)+3*x+2,{x,-5,5}]

Manipulate[Plot[a*(x^2)+b*x+c,{x,-5,5},PlotRange->{Automatic,{-50,50}}],{a,-2,2},{b,-10,10},{c,-5,5}]

ClearAll[y]
res2=DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[2*t],y[0]==1,y'[0]==0},y[t],{t}][[1]];
y=y[t]/.res2

Plot[y,{t,0,20},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"y","f (y)"}]
ClearAll[y]

ClearAll[y]
resDif=DSolve[{y''[t]+2*y'[t]+3*y[t]==Sin[2*t],y[0]==1,y'[0]==0},y[t],t];

proPlot=y[t]/.resDif[[1]];
Plot[proPlot,{t,0,20},PlotStyle->{Red,Thick,Dashed},AxesLabel->{"y","f (y)"}]

ClearAll[funkce]
funkce[x_]:=((Sin[x]*(E^x)+(x^2)-Cos[x])/((x^2)+1))

funkce[a]

b=Cos[x];

funkce[b]

funkce[x_,y_]:=x*y
funkce[{x_,y_}]:=(x/y)

funkce[a,c]
funkce[{a,c}]
funkce[a]