Question

Determine whether the following is true or false. Be sure to justify your answer!
The function sin(xy)/(xy), x and y not = 0, has a global maximum and global minimum on the set {(x, y): x^2 + y^2 <= 1, (x, y ) not = 0}

Answer 1

yes

Answer 2

pooo

Answer 3

wait it's not closed

Answer 4

can u be more specific? i still couldnt understand this

Answer 5

There's a theorem that states that continuous function have a minimum and a maximum on closed sets, but you don't have a closed set because the origin is not included.

Answer 6

man i hate this kind of question! i hope someone can help me with this, it's due tomorrow > <

Answer 7

the origin is the important point here, you need to evaluate lim x-> 0 sin(xy)/xy, if it's infinity then there's no maximum.

Answer 8

well i see what u are doing, but this is multivariable tho, e.g. it's a function of (x, y), do u mean lim as x-> 0 and y-> 0??

Answer 9

oh, yes. But maybe i'm wrong because you excluded the two axes, not just the origin.

Answer 10

anyway, wolfram alpha says there's no maximum, but there's a minimum. But as far as a proof goes I'm not that good at that.

Answer 11

k thanks for trying ... but im pretty much screwed with this problem...i wasted too much time on this already ...gonna move on