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MathQuiz 4.3
University of Sydney
School of Mathematics
and Statistics
© Copyright 2004-2006

Functions of Two Variables Quiz

Question

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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.).
There are more web quizzes at Wiley, select Section 1.

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Question 1

Consider the function $F(h,r)$ described in the table below.
Which of the following is the value of the function $F(3,4)?$

			$r$
		1	2	3	4	5
	1	3.14	12.57	28.27	50.27	78.54
	2	6.28	25.13	56.55	100.53	157.08
$h$	3	9.42	37.7	84.82	150.8	235.62
	4	12.57	50.27	113.1	201.06	314.16
	5	15.71	62.83	141.37	251.33	392.7

Not correct. Choice (a) is false.

Try again, this is $F(4,3)$ .

Not correct. Choice (b) is false.

Try again, this is $F (3,3)$ .

Not correct. Choice (c) is false.

Try again, this is $F(4,4)$ .

Your answer is correct.

This is the value in from the row labelled 3 and column labelled 4.

Question 2

Consider the function $2 2 f(x,y) = x + y - x + 3y.$ What is the value of $f(- 2,3)?$

Not correct. Choice (a) is false.

Try again, you may not have noticed that -(-2)=2.

Your answer is correct.

$2 2 f(- 2,3) = (- 2) + 3 - (- 2)+ 3× 3 = 4+ 9+ 2 + 9 = 24$

Not correct. Choice (c) is false.

Try again, this is $f(3,- 2)$ .

Not correct. Choice (d) is false.

Try again, remember the square of a negative number is a positive number.

Question 3

What is the equation of the $yz$ -plane?

Your answer is correct.

This plane allows all possible combinations of $y$ and $z$ .

Not correct. Choice (b) is false.

Try again, this is the $xz$ -plane.

Not correct. Choice (c) is false.

Try again, this is the $xy$ -plane.

Not correct. Choice (d) is false.

Try again, the $yz$ -plane takes all possible values of $y$ and $z$ .

Question 4

Find the distance $d$ between two points (1,-2,3) and (-2,3,1).

Not correct. Choice (a) is false.

Try again, remember the square of a negative number is a positive number.

Your answer is correct.

$∘ ----------------------------- d = (- 2- 1)2 + (3- (- 2))2 + (1- 3)2$	=	$√9-+-25+-4$
	=	$√38-$

Not correct. Choice (c) is false.

Try again, note that 3 - (-2)

1.

Not correct. Choice (d) is false.

Try again, remember the square of a negative number is a positive number.