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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(h,r) described in the table below.
r 1 2 3 4 5 1 3.14 12.57 28.27 50.27 78.54 26.28 25.1356.55 100.53157.08 h3 9.42 37.7 84.82 150.8 235.62 412.5750.27 113.1 201.06314.16 515.7162.83141.37251.33 392.7
Which of the following is the value of the function F(3,4) ? Exactly one option must be correct)
a)
F(3,4) = 113.1
b)
F(3,4) = 84.82
c)
F(3,4) = 201.06
d)
F(3,4) = 150.8

Choice (a) is incorrect
Try again, this is F(4,3).
Choice (b) is incorrect
Try again, this is F(3,3).
Choice (c) is incorrect
Try again, this is F(4,4).
Choice (d) is correct!
This is the value in from the row labelled 3 and column labelled 4.
Consider the function f(x,y) = x2 + y2 x + 3y. What is the value of f(2,3)? Exactly one option must be correct)
a)
f(2,3) = 20
b)
f(2,3) = 24
c)
f(2,3) = 4
d)
f(2,3) = 16

Choice (a) is incorrect
Try again, you may not have noticed that -(-2)=2.
Choice (b) is correct!
f(2,3) = (2)2 + 32 (2) + 3 × 3 = 4 + 9 + 2 + 9 = 24
Choice (c) is incorrect
Try again, this is f(3,2).
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 (1,2,3) and (2,3,1). Exactly one option must be correct)
a)
d = 20
b)
d = 38
c)
d = 14
d)
d = 12

Choice (a) is incorrect
Try again, remember the square of a negative number is a positive number.
Choice (b) is correct!
d = (2 1)2 + (3 (2))2 + (1 3)2 = 9 + 25 + 4 = 38
Choice (c) is incorrect
Try again, note that 3 (2)1.
Choice (d) is incorrect
Try again, remember the square of a negative number is a positive number.