7.
	|r(t)|=sqrt(sin(t)^2+cos(t)^2+16t^2)=sqrt(1+16t^2)
	r'(t)=cos(t)*e_1+4*e_2-sin(t)*e_3
	|r'(t)|=sqrt(cost(t)^2+16+(-sin(t))^2)=sqrt(17)
	r''(t)=-sin(t)*e_1+0*e_2+(-cos(t))*e_3
	|r''(t)|=sqrt((-cos(t))^2+(-sin(t))^2)=sqrt(1)=1
	
	|r(0,5)|=sqrt(5)
	r'(0,5)=cos(0,5)*e_1+2*e_2-sin(0,5)*e_3
	|r(0,5)|=sqrt(17)
	r''(0,5)=-sin(0,5)*e_1+0*e_2-cos(0,5)*e_3
	|r''(0,5)|=1
8.
	a)
		s(t) = intgr(|r'(t)|)
		r'(t) = b*cos(t)*e_1-(a+b)*e_2+(b*sin(t))*e_3
		|r'(t)| = sqrt(b^2cos(t)^2+(a+b)^2+b^2sin(t)^2) = sqrt(2b^2+a^2+2ab)
		intgr[0,t'](|r'(t)|) = t*sqrt(a^2+2ab+2b^2)
	b)
		e_t(t) = r'(t)/s(t) = (b*cos(t)*e_1-(a+b)*e_2+(b*sin(t))*e_3)/sqrt(2b^2+a^2+2ab)
		t(s) = s(t)^-1 = s/sqrt(2b^2+a^2+2ab)
		e_t(s) = e_t(t(s))= (b*cos(s/sqrt(2b^2+a^2+2ab))*e_1-(a+b)*e_2+(b*sin(s/sqrt(2b^2+a^2+2ab)))*e_3)/sqrt(2b^2+a^2+2ab)
	c)
		Z:=1/sqrt(2b^2+a^2+2ab)
		e_n(s)=e_t'(s)/|e_t'(s)|
		=((b*Z * -sin(s*Z))*e_1+0*e_2+(b*Z *cos(s*Z))*e_3)*Z
		/ sqrt(b^2*Z^2*(-sin(s*Z))^2+b^2*Z^2*cos(s*Z)^2)*sqrt(Z)
		= (...) / sqrt(b^2*Z^2)=(...)/bZ
		= (Z*-sin(s*Z))*e_1+0*e_2+(Z*cos(s*Z))*e_3
	d)
		e_b(s)=e_t(s) x e_n(s)
		=e_1*(-(a+b)*Z*(Z*cos(s*Z))-0) + e_2*((b*sin(s*Z))*Z*(Z*-sin(s*Z)-b*cos(s*Z)*Z*(Z*cos(s*Z))) + e_3*(0+(a+b)*Z*(Z*-sin(s*Z)))
		=Z^2 * (e_1*((a+b)*cos(s*Z)) + e_2*(-b*(sin(ZT)^2+cos(ZT)^2)) +e_3*((a+b)*-sin(s*Z))
		=Z^2 * (e_1*((a+b)*cos(s*Z)) - e_2*b - e_3*((a+b)*sin(s*Z)))
	e)
		Da e_b(s) = e_t(s) x e_n(s), ist e_b(s) auf e_t(s) und e_n(s) senkrecht.
		z.Z: e_t(s) * e_n(s) = 0
		=((b*cos(s*Z)*e_1-(a+b)*e_2+(b*sin(s*Z))*e_3)*Z)*((Z*-sin(s*Z))*e_1+0*e_2+(Z*cos(s*Z))*e_3)
		=(b*Z*cos(s*Z)*(Z*-sin(s*Z)) -(a+b)*Z*0 + (b*Z*sin(s*Z))*(Z*cos(s*Z))
		=-bZ^2cos(sZ)sin(sZ)-0+bZ^2sin(sZ)cos(sZ)
		=0
		q.e.d.
	f)	
		a(t)=r''(t)=-b*sin(t)*e_1+0*e_2+(b*cos(t))*e_3

9.
	a)
		U (radiale abhngigkeit)
		Kreise mit Rand-Konvergenz (Hhenlienie)
	b)
		(x_1,0,x_3) <=> x_2=0
		(0,x_2,x_3) <=> x_1=0
		x_3 = sqrt(1 - x_1^2/4 - x_2^2/25)
		
		Schnittkurve 1: x_3 = sqrt(1 - x_1^2/4)
		Schnittkurve 2: x_3 = sqrt(1 - x_2^2/25)