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.