g[x_]:=Tan[x]

g[5]

NumberForm[g[3.0],12]

Plot[g[x],{x,-4,4}]

N[Limit[g[x],x->1],4]

Limit[g[x],x->Pi/2,Direction ->1]

Limit[g[x],x->Pi/2, Direction -> -1]

Limit[1/(x-1)^2,x->1]

Plot[g[x],{x,-4,4},PlotRange->{-20,20}]

G1[x_,h_]:= ( (x+h)^2 - x^2)/h;

Plot[G1[x,0.5],{x,-5,5}]

Plot[{G1[x,2],G1[x,1],G1[x,0.2],G1[x,0.01]},{x,-5,5}]

This graph shows four curves that appear to be straight lines.

G2[x_,h_]:= ( (x+h)^3 - x^3)/h;

Plot[{G2[x,2],G2[x,1],G2[x,0.2],G2[x,0.01]},{x,-4,4}]

G3[x_,h_]= ( Log[x+h] - Log[x])/h

Plot[G3[x,0.001],{x,0.0001, 5}]

Plot[{G3[x,1],G3[x,0.5], G3[x,0.25],G3[x,0.125],1/x},{x,0.0001,5}]

G4[x_]:=x^2 * Sin[1/x]

Plot[G4[x],{x,-0.1,0.1}]

G5[x_]:=x^2;G6[x_]:=-x^2;

Plot[{G4[x],G5[x],G6[x]},{x,0.0001,.01},PlotRange->{-0.0001,0.0001}]

Plot[(x+2)/(x^2-4),{x,-2.1,-1.99}]

f[x_]:=Cos[Pi*x]

Plot[f[x],{x,-10,10}]

Ahhhggh!  What is this?  Maybe be careful if you decide to use 'Free Form Input' format ...