Comparing Functions and their Taylor Polynomials

taylorpoly[f_,x_,a_,n_] := Normal[Series[f[y],{y,a,n}]]/.y -> x

f1[x_] := Log[1 + x]

g1[x_,n_] := taylorpoly[f1,x,0,n]

f2[x_] := Exp[x]
g2[x_,n_] := taylorpoly[f2,x,0,n]

f3[x_] := Sin[x]
g3[x_,n_] := taylorpoly[f3,x,0,n]

g3[x,5]

Manipulate[Plot[Tooltip[{f1[x],g1[x,n]}],{x,-1,1.5}, PlotRange -> {-1,1.5}, PlotStyle->Thick],{n,1,8,1}]

Manipulate[Plot[Tooltip[{f2[x],g2[x,n]}],{x,-1,3}, PlotRange -> {0,27}, PlotStyle->Thick],{n,1,8,1}]

Manipulate[Plot[Tooltip[{f3[x],g3[x,n]}],{x,-Pi,4 Pi}, PlotRange -> {-1,1}, PlotStyle->Thick],{n,1,8,1}]