Exercise 1 | Wiskunde op Tilburg University

Which of the following graphs depicts the level curves of

$z(x,y)=x^2 + y$ with values

$k=4$ and

$k=10$ ?

Antwoord 1 correct

Correct

Antwoord 2 optie

Antwoord 2 correct

Fout

Antwoord 3 optie

Antwoord 3 correct

Fout

Antwoord 4 optie

Antwoord 4 correct

Fout

Antwoord 1 optie

Antwoord 1 feedback

Correct: The rewriting of

$x^2 + y = k$ for

$k=4$ gives:

$x^2 + y = 4 \iff y = 4-x^2.$
This is a downward opened parabola that intersects the

$y$ -axis at

$(0,4)$ and the

$x$ -axis at

$(-2,0)$ and

$(2,0)$ . Consequently, it is the lower curve of the two. The rewriting of

$x^2 + y = k$ for

$k=10$ gives:

$x^2 + y = 10 \iff y = 10-x^2.$
This is a downward opened parabola that intersects the

$y$ -axis at

$(0,10)$ and the

$x$ -axis at

$(-\sqrt{10},0)$ and

$(\sqrt{10},0)$ . Consequently, it is the uppercurve of the two.

Go on.

Antwoord 2 feedback

Wrong: Pay attention when rewriting

$z(x,y)=k$ .

See Example 1 and Example 2.

Antwoord 3 feedback

Wrong: Pay attention when rewriting

$z(x,y)=k$ .

See Example 1 and Example 2.

Antwoord 4 feedback

Wrong: Level curves cannot intersect.

See Level curves, Example 1 and Example 2.