Elementárne funkcie

Plot[Exp[x],{x,-3,3}]

Plot[{Exp[x],Exp[0.5x],Exp[2x]},{x,-3,3}]

Plot[{Exp[x],Exp[0.5x],Exp[2x]},{x,-3,3},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Plot[{Exp[-x],Exp[-0.5x],Exp[-2x]},{x,-2,2},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Plot[{(E^(-x)),(E^(-0.5 x)),(E^(-2 x))},{x,0,5},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Manipulate[Plot[Exp[c x],{x,-3,3},PlotRange->{0,10}],{c,1,2}]

Manipulate[Plot[Exp[c x],{x,-3,3},PlotRange->{0,10}],{c,-2,2}]

Plot[Exp[-x^2],{x,-3,3},PlotStyle->RGBColor[1,0,0]]

Plot[{Exp[x],Log[x],x},{x,-3,3},PlotRange->{-3,3},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Plot[{Exp[0.5x],2Log[x],x},{x,-3,3},PlotRange->{-3,3},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

f1[x_]:=Exp[0.5x];
f2[x_]:=2Log[x];
Clear[z];
f1[f2[z]]

f1[f2[2]]

f2[f1[2]]

Plot[{Log[x],Log[2,x],Log[10,x]},{x,0.1,5},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Plot[{2^x,Log[2,x],x},{x,-3,3},PlotRange->{-3,3},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Plot[{10^x,Log[10,x],x},{x,-3,3},PlotRange->{-3,3},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Manipulate[Plot[Sin[c x],{x,0,2 Pi}],{c,1,10,1}]

Manipulate[Plot[Sin[c x],{x,0,2 Pi}],{c,1,10}]

Manipulate[Plot[Sin[x+c],{x,0,2 Pi}],{c,0,Pi}]

Manipulate[Plot[{Sin[x+c],Cos[x+c]},{x,0,2 Pi}],{c,0,Pi}]

Manipulate[Plot[{Sin[x+c],Cos[x-Pi/4+c]},{x,0,2 Pi}],{c,0,Pi}]

Plot[{Cos[x],Cos[2x],Cos[3x]},{x,0,2Pi},PlotStyle->{RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]},ImageSize->{400,400}]

Plot[{Sin[x],ArcSin[x],x},{x,-1,1},PlotRange->{-Pi/2,Pi/2},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Plot[{Sin[x],ArcSin[x],x},{x,-3,3},PlotRange->{-Pi/2,Pi/2},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Manipulate[N[Sin[x]/x],{x,1,0.1,-0.1}]

Do[Print[N[Sin[x]/x]],{x,1,0.1,-0.1}]

Manipulate[N[Sin[x]/x],{x,1,0.01,-0.01}]

Clear[x]

Limit[Sin[x]/x,x->0]

Plot[Sin[x]/x,{x,0,10Pi},PlotStyle->RGBColor[1,0,0],ImageSize->{400,400},PlotRange->All]

Do[Print[N[(1+1/n)^n]],{n,1,10,1}]

Manipulate[N[(1+1/n)^n],{n,1,1000,1}]

E//N

Plot[{Tan[x],ArcTan[x],x},{x,-5,5},PlotRange->{-5,5},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1],RGBColor[0,1,0]},AspectRatio->Automatic,ImageSize->{400,400}]

Simplify[Cos[x]^2+Sin[x]^2]

Clear[x,y]
Needs["Graphics`ImplicitPlot`"]
ImplicitPlot[x^2+y^2==1,{x,-3,3}]
ImplicitPlot[x^2-y^2==1,{x,-3,3}]

Manipulate[ImplicitPlot[x^2+y^2==c,{x,-1,1},PlotRange->{{-1,1},{-1,1}}],{c,0,1}]

Manipulate[ImplicitPlot[x^2-y^2==c,{x,-1,1},PlotRange->{{-1,1},{-1,1}}],{c,0,1}]

D[Exp[x],x]

Manipulate[Plot[Evaluate[D[Exp[x],{x,c}]],{x,-3,3}],{c,0,5,1}]

Manipulate[Plot[Evaluate[D[Sin[x],{x,c}]],{x,0,2Pi}],{c,0,12,1}]