g[x_]:=x * Sin[x]

g[5]

NumberForm[g[5.0],12]

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

Plot[g[x],{x,-4,4},PlotRange->{-2,5}]

N[Limit[g[x],x->3*Pi/2],12]

G1[x_,h_]:=( 5^(x+h) - 5^x)/h

Plot[G1[x,1],{x,-2,2}]

Plot[{G1[x,2],G1[x,1],G1[x,0.125],5^x * Log[5]},{x,-2,2}]

G2[x_,h_]= ( Sqrt[x+h] - Sqrt[x])/h

Plot[G2[x,0.001],{x,0, 5}]

Plot[{G2[x,1],G2[x,0.5], G2[x,0.25],G2[x,0.125],1/(2*Sqrt[x])},{x,0,5}]

G3[x_]:=Sin[1/x]

Plot[G3[x],{x,0.001,.1}]

G4[x_]:=x^2*Sin[1/x];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,-4,4}]