2.2 Mängder

Övning 3.2.1

Skissa parablerna.

a) \displaystyle y=2(x+1)^2.

b) \displaystyle x=2y^2.

Övning 3.2.2

Skissa ellipserna

a) \displaystyle 4x^2+\frac{1}{9}y^2=1.

b) \displaystyle \frac{(x+1)^2}{9}+\frac{(y-2)^2}{4}=1.

c) \displaystyle x^2+y^2+2x-4y=1

Övning 3.2.3

Skissa hyperblerna

a) \displaystyle x^2-y^2=1.

b) \displaystyle 4x^2-\frac{1}{9}y^2=1.

c) \displaystyle 4x^2-\frac{1}{9}y^2=-1

Övning 3.2.4

Rita följande mängder

a) \displaystyle \{(x,y)\in\mathbb{R}^2:\, 4x^2+\frac{1}{9}y^2<1\}.

b) \displaystyle \{(x,y)\in\mathbb{R}^2:\ 4x^2+\frac{1}{9}y^2\ge 1\}.

c) \displaystyle \{(x,y)\in\mathbb{R}^2:\, x\le 2y^2\}

d) \displaystyle \{(x,y)\in\mathbb{R}^2:\, x^2-y^2>1,\ 2x-y<3 ,\ x>0\}

e) \displaystyle \{(x,y\in\mathbb{R}^2:\, y< x$, $x^2+y^2\le 1\}

f) \displaystyle \{(x,y)\in\mathbb{R}^2:\, 4x^2+\frac{1}{9}y^2<1,\ y\ge -x\}