Recent content by mathie_geek

Oh, I see. Since \displaystyle \frac{ad+bc-cd}{d}> \displaystyle \frac{ad+bc-cd}{cd} then does that mean it HAS to = 0? If it's 0 then lim is 1/2

I got this after: (|x|^{a+(bc/d)-c}) /{2} expanding the exponents I have \displaystyle \frac{acd+bc^2-c^2d}{cd} and given \displaystyle \frac{ad+bc-cd}{cd}<=0 which is 1/c of the exponent.. So then |x| has an exponent negative so limit d.n.e right? cause limit of 1/|x| as x->0 d.n.e

I let ##y = x^(c/d)## so that it simplifies to ##(|x|^ (a+(bc/d)))/2(|x|^c)## which as x->0 limit becomes 0/2 ? I'm not sure how to take into account the inequality of a,b,c,d though

I tried that but I don't know why it didn't work out for me because I kept getting 0 as the limit..

OH, I let y= t^(1/d) and x=t^(1/c) so that lim t->0 (|t|^a/c+b/d-1)/2 and since a/c+b/d-1 <= 0, then the limit would be 1/2 if a/c+b/d-1=0 or does not exist if a/c+b/d-1< 0. since the two limits do not agree, limit d.n.e. Is this correct? :D

ok, I tried x = t^(d/c) and y = t^(c/d) as two different limits so I got: lim y->0 (|t|^ad/c)(|y|^b)/((|t|^d)+(|y|^d)) lim x->0 ((|x|^a)(|t|^bc/d))/((|x|^c)+(|t|^c)) those both =0 though. I'm sorry I'm not that good at this. Do you mean to put both of the substitutions into one limit of...

I got lim y->0 ((|t|^ap)(|y|^b))/((|t|^pc)+|y|^d)) = 0 and lim x->0 ((|x|^a)(|t|^bq)/((|x|^c)+(|t|^dq)) = 0 Did I do something wrong?

It's (a/c)+(b/d) <= 1 can anyone help

Thanks! Trying to learn how to input functions :P I missed a + so denominator is |x|^c + |y|^d

Homework Statement I need to prove a limit does not exist for f(x,y) as (x,y) -> (0,0). I already tried approaching from y=mx and I got the limit 0. Homework Equations f(x,y) = ((|x|^a)(|y|^b))/((|x|^c)+(|y|^d)) where a,b,c,d are positive numbers and a/c+b/d ≤ 1 The Attempt at a Solution I got...