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Find the domain and range of the function. `f(x,y) = x/y`
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it's defined `D=<<AA x in RR >> xx<< AA y in RR | y!=0 >>`
We se function is not limited for, x wit a finte value and y too much close to zero on the left or right the function has greater module values :
`lim_(y->0^+) f(x,y)= -oo` `lim_(y->0^-) f(x;y)= +oo`
On the other side, for y with a finte value , and x approaching to zero:
So the range of `f(x,y)` is `(-oo;+oo)`
This graph is projection f(x;y) wich every colored line stands for a fixed x value.
It's show function graph is a hiperbolyc parapholoid
Posted by oldnick on May 24, 2013 at 4:11 AM (Answer #1)
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