# R-Code fuer Aufgabe 3:

# 3a)

n = 10
x = seq(-3,3,by=0.005)
nx = length(x)
y = exp(x)

mycol = rev(rainbow(1.7*n)[1:n])     # Farbpalette mit n Farben

en = rep(0,nx)
info = "e^x und e_n(x), e^x in black"
plot(x, y, main=info, font.main=10, ylim=c(-2,8) )
for(j in 0:n)
{
  en = en + x^j/factorial(j) 
  points(x, en, col=mycol[j+1], cex=0.2 )       # cex = character expansion
}

# 3b)

par(mfrow=c(1,2))     # 2 Diagramme in einem Plot-Fenster

n = 10
x = seq(-2*pi,2*pi,by=0.005)
nx = length(x)
y = sin(x)

sn = rep(0,nx)
info = "sin(x) und s_n(x), sin(x) in black"
plot(x, y, main=info, font.main=10, ylim=c(-4,4) )
for(k in 0:n)
{
  sn = sn + (-1)^k * x^(2*k+1)/factorial(2*k+1) 
  points(x,sn,col=mycol[k+1],cex = 0.2) 
}

# 3c)

n = 10
x = seq(-2*pi,2*pi,by=0.005)
nx = length(x)
y = cos(x)

cn = rep(0,nx)
info = "cos(x) und c_n(x), cos(x) in black"
plot(x, y, main=info, font.main=10, ylim=c(-4,4) )
for(k in 0:n)
{
  cn = cn + (-1)^k * x^(2*k)/factorial(2*k) 
  points(x,cn,col=mycol[k+1],cex = 0.2) 
}