Practice: Several Variables

10 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

Domain of

f (x, y) = \frac{1}{x - y}

Q2.

basic

Closely spaced contours indicate

Q3.

basic

Level curves of

f (x, y) = x^{2} + 4 y^{2}

at positive

c

are

Q4.

basic

Level surfaces of

f (x, y, z) = x^{2} + y^{2} + z^{2}

are

Q5.

basic

The trace of

z = x^{2} + y^{2}

z = 4

Q6.

basic

Which surface is described by

z = x^{2} + y^{2}

Q7.

intermediate

True/False: Every equation in

x, y, z

defines

z

as a function of

(x, y)

Q8.

intermediate

Domain of

f (x, y) = ln (y - x^{2})

Q9.

basic

Match:

z = e^{- (x^{2} + y^{2})}

has

Q10.

advanced

On a contour map of

f (x, y)

, two contours that cross indicate