## MATH1111 Quizzes

Functions of Two Variables Quiz
Web resources available Questions

This quiz tests the work covered in the lecture on Functions of Two Variables and corresponds to Section 12.1 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).

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Consider the function $F\left(h,r\right)$ described in the table below.
$\begin{array}{ccccccc}\hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill r\hfill & \hfill \hfill & \hfill \hfill \\ \hfill \hfill & \hfill \phantom{\rule{1em}{0ex}}\hfill & \hfill 1\hfill & \hfill 2\hfill & \hfill 3\hfill & \hfill 4\hfill & \hfill 5\hfill \\ \hfill \hfill & \hfill 1\hfill & \hfill 3.14\hfill & \hfill 12.57\hfill & \hfill 28.27\hfill & \hfill 50.27\hfill & \hfill 78.54\hfill \\ \hfill \hfill & \hfill 2\hfill & \hfill 6.28\hfill & \hfill 25.13\hfill & \hfill 56.55\hfill & \hfill 100.53\hfill & \hfill 157.08\hfill \\ \hfill h\hfill & \hfill 3\hfill & \hfill 9.42\hfill & \hfill 37.7\hfill & \hfill 84.82\hfill & \hfill 150.8\hfill & \hfill 235.62\hfill \\ \hfill \hfill & \hfill 4\hfill & \hfill 12.57\hfill & \hfill 50.27\hfill & \hfill 113.1\hfill & \hfill 201.06\hfill & \hfill 314.16\hfill \\ \hfill \hfill & \hfill 5\hfill & \hfill 15.71\hfill & \hfill 62.83\hfill & \hfill 141.37\hfill & \hfill 251.33\hfill & \hfill 392.7\hfill \end{array}$
Which of the following is the value of the function $F\left(3,4\right)$ ? Exactly one option must be correct)
 a) $F\left(3,4\right)=113.1$ b) $F\left(3,4\right)=84.82$ c) $F\left(3,4\right)=201.06$ d) $F\left(3,4\right)=150.8$

Choice (a) is incorrect
Try again, this is $F\left(4,3\right)$.
Choice (b) is incorrect
Try again, this is $F\left(3,3\right)$.
Choice (c) is incorrect
Try again, this is $F\left(4,4\right)$.
Choice (d) is correct!
This is the value in from the row labelled 3 and column labelled 4.
Consider the function $f\left(x,y\right)={x}^{2}+{y}^{2}-x+3y\phantom{\rule{0.3em}{0ex}}.$ What is the value of $f\left(-2,3\right)$? Exactly one option must be correct)
 a) $f\left(-2,3\right)=20$ b) $f\left(-2,3\right)=24$ c) $f\left(-2,3\right)=4$ d) $f\left(-2,3\right)=16$

Choice (a) is incorrect
Try again, you may not have noticed that -(-2)=2.
Choice (b) is correct!
$f\left(-2,3\right)={\left(-2\right)}^{2}+{3}^{2}-\left(-2\right)+3×3=4+9+2+9=24$
Choice (c) is incorrect
Try again, this is $f\left(3,-2\right)$.
Choice (d) is incorrect
Try again, remember the square of a negative number is a positive number.
What is the equation of the $yz$-plane? Exactly one option must be correct)
 a) $x=0$ b) $y=0$ c) $z=0$ d) $y+z=0$

Choice (a) is correct!
This plane allows all possible combinations of $y$ and $z$.
Choice (b) is incorrect
Try again, this is the $xz$-plane.
Choice (c) is incorrect
Try again, this is the $xy$-plane.
Choice (d) is incorrect
Try again, the $yz$-plane takes all possible values of $y$ and $z$.
Find the distance $d$ between two points $\left(1,-2,3\right)$ and $\left(-2,3,1\right)$. Exactly one option must be correct)
 a) $d=\sqrt{20}$ b) $d=\sqrt{38}$ c) $d=\sqrt{14}$ d) $d=\sqrt{12}$

Choice (a) is incorrect
Try again, remember the square of a negative number is a positive number.
Choice (b) is correct!
$d=\sqrt{{\left(-2-1\right)}^{2}+{\left(3-\left(-2\right)\right)}^{2}+{\left(1-3\right)}^{2}}=\sqrt{9+25+4}=\sqrt{38}$
Choice (c) is incorrect
Try again, note that $3-\left(-2\right)\ne 1.$
Choice (d) is incorrect
Try again, remember the square of a negative number is a positive number.