Equation question: t=f(x,y)=arctan(x/y)

[v9260019]

an equation question

Hello all
If let t=f(x,y)=arctan(x/y)
does t exist when y=0 or limt[y->0] ????
thanks a lot

 

[xaris106]

Re: an equation question

if i remember correct you must define x as a constant(not always)
edit*wrong*
then you approach y>0 from possitives and from negatives and if the limit is the same it exists.

 

[alitavakol]

Re: an equation question

if x≠0 then its limit will be π/2. and if x=0 then this will be 0.
so lim f(x, y) for y->0 will have a discontinuty at x=0.