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(1 point) Each of the following functions has a maximal domain on which it is co

ID: 2890886 • Letter: #

Question

(1 point) Each of the following functions has a maximal domain on which it is continuous and that domain has a boundary. Match the verbal description of this boundary with the function by putting the letter corresponding to the boundary to the left of the letter labelling the function. 1 1.f(x, y, z) = x2 + y2 +22 2. f(x, y, z) = 1 - 72 - y2 3. f(x, y) = 4 - x2 - ya 4. f(x, y) = e(x-y) xyz 5. f(x, y, z) = x2 + y2 - Z A. a circular cylinder B. a straight line C. a circular parabaloid D. a circle E. one point

Explanation / Answer

1)

f(x,y,z) is undefined when x2+y2+z2=0

x2+y2+z2=0 satisfies only at point (x,y,z)=(0,0,0)

E. one point

2)

f(x,y,z) is undefined when 1-x2-y2=0

=>x2+y2=1 represents circular cylinder of radius 1 with z-axis as its axis

A. a circular cylinder

3)

f(x,y) is undefined when 4-x2-y2=0

=>x2+y2=4 represents circle with radius 2

D .a circle

4)

f(x,y) is undefined when x-y=0

=>y =x

B. a straight line

5)

f(x,y,z) is undefined when x2+y2-z=0

=>z = x2+y2 represents circular paraboloid with z-axis as its axis

C. a circular paraboloid

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