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find domain in xy plane

function f(x,y)=log(xsiny)

find the domain in the xy-plane in which f(x,y) can be defined as a real-valued function. sketch this domain in the xy-plane in the region
-2pi < x< 2pi , -2pi < y <2pi.
Reply 1
Avatar for nota bene
nota bene
15
log(u) is real for u>0

0≤x≤2π0\le x\le2\pi combined with 0≤y≤π0\le y\le\pi [edit: there is obviously the equivalent−2π≤y≤−π-2\pi\le y \le-\pi] gives real values, as does:
−2π≤x≤0-2\pi\le x\le0 combined with −π≤y<0-\pi\le y<0 [edit: here there is the equivalent π≤y<2π\pi\le y<2\pi]also give real values. I think these are all combinations.

Does this help you?
Reply 2
Avatar for Notnek
Notnek
21
nota bene
log(u) is real for u>0

0≤x≤2π0\le x\le2\pi combined with 0≤y≤π0\le y\le\pi [edit: there is obviously the equivalent−2π≤y≤−π-2\pi\le y \le-\pi] gives real values, as does:
−2π≤x≤0-2\pi\le x\le0 combined with −π≤y<0-\pi\le y<0 [edit: here there is the equivalent π≤y<2π\pi\le y<2\pi]also give real values. I think these are all combinations.

The domain in the xy plane would be xsiny>0 though.
Reply 3
Avatar for nota bene
nota bene
15
notnek
The domain in the xy plane would be xsiny>0 though.

Yes, and that's surely what I've written:confused:

i.e. my first line reads: "let x vary between 0 and 2pi at the same time as letting y vary between 0 and pi OR y vary between -2pi and -pi."
Reply 4
Avatar for choccookies
choccookies
OP
thats what i got for the domain, but how would i sketch this? in the region? what would the boundary lines be?
Reply 5
Avatar for Notnek
Notnek
21
nota bene
Yes, and that's surely what I've written:confused:

i.e. my first line reads: "let x vary between 0 and 2pi at the same time as letting y vary between 0 and pi OR y vary between -2pi and -pi."

Sorry it's just that i've already done this question and was just checking if my answers are correct.

I agree with you about the combinations.
Reply 6
Avatar for choccookies
choccookies
OP
i still dont understand how to draw it including the boundary lines...
Reply 7
Avatar for Notnek
Notnek
21
choccookies
i still dont understand how to draw it including the boundary lines...

Nota bene told you the regions that you need to shade in your graph so I don't see your problem.
Reply 8
Avatar for choccookies
choccookies
OP
sorry, this is the first time im trying a question like this,am i drawing the graph of xsiny and shading in the regions?

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