Exercise 2 | Wiskunde op Tilburg University

The function $z(x,y)$ is given by $z(x,y)=y\ln(x)-xe^y$ . Determine the slope of the line tangent to the level curve through the point $(1,0)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$0$

Antwoord 2 correct

Fout

Antwoord 3 optie

$1$

Antwoord 3 correct

Fout

Antwoord 4 optie

The slope is not defined in that point.

Antwoord 4 correct

Fout

Antwoord 1 optie

None of the other answers is correct.

Antwoord 1 feedback

Correct: $\begin{align*} \dfrac{z'_x(x,y)}{z'_y(x,y)}&= \dfrac{\frac{y}{x}-e^y}{\ln(x)-xe^y}. \end{align*}$

$\begin{align*} \textrm{slope} &=- \dfrac{\frac{0}{1}-e^0}{\ln(1)-1\cdots^0}\\ &=-\dfrac{-1}{-1}\\ & = - 1. \end{align*}$

Go on.

Antwoord 2 feedback

Wrong: $e^0\neq 0$ .

Try again or see Exponential functions.

Antwoord 3 feedback

Wrong: The slope is not equal to the quotient of the partial derivatives.

See Tangent line level curve.

Antwoord 4 feedback

Wrong: $z'_y(x,y)=\ln(x)-xe^y$ .

Try again.