Lösungen Test 1 B1

1

a

I = (-4, Infinity)

b

I = { }

c

Kein Plot möglich (Plot[Sqrt[5-x],{x,...,... }];)

2

(b^(Sqrt[8])/b^(Sqrt[2]))^(Sqrt[2]/Sqrt[3])+Log[Log[E^b]]+Log[Log[E^(2 b)]]//PowerExpand

Resultat:

3

a

Solve[25x^2+4 b x+16==0,{x}] //Flatten

Solve[-100 + b^2==0,{b}] //Flatten

b

Solve[Sqrt[x^4+9]==x^2+1,{x}] //Flatten

25x^2+4 b x+16/.{b->10,x->2}

25x^2+4 b x+16/.{b->10,x->-2}

25x^2+4 b x+16/.{b->-10,x->2}

25x^2+4 b x+16/.{b->-10,x->-2}

4

Automatische Lösung

g1=(2 x1+x2==1*7);
g2=(3 x2+x3==4*7);
g3=( x3-x4==3*7);
g4=(x4+x1 Sign[x1]==0);
Solve[{g1,g2,g3,g4},{x1,x2,x3,x4}] //Flatten

Lösung für positive x1

g4=(x4+x1==0);
Solve[{g1,g2,g3,g4},{x1,x2,x3,x4}] //Flatten

Lösung für negative x1

Falls x1 < 0: Keine Lösung, da x1 > 0 herauskommt!

g4=(x4-x1==0);
Solve[{g1,g2,g3,g4},{x1,x2,x3,x4}] //Flatten

5

Lösung

Solve[((x-1)^2)/4+((x-1-1)^2)/9==1,{x}] //Flatten

solv=Solve[((x-1)^2)/4+((x-1-1)^2)/9==1,{x}]//N  //Flatten

Graphik

x1=x/.solv[[1]];x2=x/.solv[[2]]; {x1,x2}

<< Graphics`ImplicitPlot`

p1=ImplicitPlot[(x-1)^2 /4 + (y-1)^2 / 9 ==1,{x,-1,3},AspectRatio->Automatic,DisplayFunction:>Identity];

g[x_]:=0+(x-1)

p2=Plot[g[x],{x,-1,3},Epilog->{PointSize[0.03],Point[{x1,g[x1]}],Point[{x2,g[x2]}]},AspectRatio->Automatic,DisplayFunction:>Identity];

Show[p2,p1,DisplayFunction:>$DisplayFunction];

6

a

Plot[(3x+2)/(x+1),{x,-4,4}];

Keine der Eigenschaften

b

Plot[-E^{-x}+4+Cos[x],{x,-5,15}];

Keine der Eigenschaften

c

Plot[x Sqrt[x^2+16],{x,-10,10}];

Ungerade

7

Limit[(2n^2+3n+1)/(5n^2),{n->Infinity}]