Thread: Functions of several variables

1. Functions of several variables

The problem states:
A function f(x,y) is defined on the disc Q: x^2+y^2<=1 and equals 1 on it. The domain of f is D(f)=Q and f(x,y)=1 on Q.

The graph of the function is made of steel and hangs in the air. There is a flower at the origin and a few bees are in the air. There current positions are listed below.
Hint: If the bee is at the height z>1, where should is be in order not to see the flower?

Which of these bees can see the flower?

a) (4,5,6)
b) (2,3,4)
c) (6,6,9)
d) (0,1,2)
e) (2,1,3)
f) (1/3,1/3,1/3)

Not sure what this problem is asking, or how to start.

2. Re: Functions of several variables

The bee cannot see through the disc. So its line of sight to the origin must not intersect the graph of the function. If the bee's z-coordinate is less than 1 there is no problem: the bee can certainly see the flower. But if the bee's z-coordinate is greater than 1 then the disc may get in the way. Find the equation of the line from the bee's position to the origin and check where that line meets the plane z=1.