set terminal postscript

set style line 1 lw 3
set style line 2 lw 3
set style line 3 lw 3
set style line 4 lw 3
set style line 5 lw 3
set style line 6 lw 3
set style line 7 lw 3
set style line 8 lw 3

set output "sinus.ps"
set title "Taylor-Entwicklung von sin x"
plot [x=-3*pi:3*pi] [-2:2] \
  sin(x) w l lw 3 title "sin x", \
  x w l lw 3 title "T(1)", \
  x-(x**3)/6 w l lw 3 title "T(3)", \
  x-(x**3)/6+(x**5)/120 w l lw 3 title "T(5)", \
  x-(x**3)/6+(x**5)/120-(x**7)/5040 w l lw 3 title "T(7)", \
  x-(x**3)/6+(x**5)/120-(x**7)/5040+(x**9)/362880 w l lw 3 title "T(9)", \
  x-(x**3)/6+(x**5)/120-(x**7)/5040+(x**9)/362880-(x**11)/39916800 w l lw 3 title "T(11)", \
  x-(x**3)/6+(x**5)/120-(x**7)/5040+(x**9)/362880-(x**11)/39916800+(x**13)/6227020800 w l lw 3 title "T(13)"

set output "e.ps"
set title "Taylor-Entwicklung von e^x"
plot [x=-1:3] \
  exp(x) w l lw 3 title "e^x", \
  1+x w l lw 3 title "T(1)", \
  1 + x + (x**2)/2 + (x**3)/6 + (x**4)/24 + (x**5)/120 w l lw 3 title "T(5)", \
  1 + x + (x**2)/2 + (x**3)/6 + (x**4)/24 + (x**5)/120 + (x**6)/720 + (x**7)/5040 + (x**8)/40320 + (x**9)/362880 + (x**10)/3628800 w l lw 3 title "T(10)"

set output "sinx.ps"
set title "Taylor-Entwicklung von (sin x)/(x+1)"
plot [x=-2*pi:2*pi] [-1.2:1.2] \
  sin(x)/(x+1) w l lw 3, \
  (-305353)*x**10/362880+305353*x**9/362880+(-4241)*x**8/5040+4241*x**7/5040+(-101)*x**6/120+101*x**5/120+(-5)*x**4/6+5*x**3/6-x**2+x  w l lw 3 title "T(10)",\
  -4.108911369468592E-4*(x-1.0)**10+8.215503870482579E-4*(x-1.0)**9-.0016416118457845*(x-1.0)**8+.0033040935076604*(x-1.0)**7-.0067153898537868*(x-1.0)**6+.0122620700064515*(x-1.0)**5-.0200216207973352*(x-1.0)**4+.0751045326283327*(x-1.0)**3-0.240259449568022*(x-1.0)**2+.0597834067320958*(x-1.0)+.4207354924039483 w l lw 3 title "T1(10)"