1. The problem statement, all variables and given/known data Prove that if g:R->R is continuous at a then f(x,y)=g(x) is continuous at (a,b) [tex]\forall[/tex] b [tex]\in[/tex] R 2. Relevant equations 3. The attempt at a solution So we know [tex]\forall[/tex]e>0 [tex]\exists[/tex]d>0 s.t. [tex]\forall[/tex]x[tex]\in[/tex]R where |x-a|<d we have |g(x) - g(a)|<e So I've said as [tex]\forall[/tex]b[tex]\in[/tex]R g(x)=f(x,y) & g(a)=f(a,b), these can be substituted in giving the expression we need except for the condition that [(x-a)2 + (y-b)2]1/2<d. This seems to be an incorrect cheat though, am I along the right lines or not?