1. The problem statement, all variables and given/known data Hey guys, I've been given the following [itex] \epsilon - \delta [/itex] proof question. The trouble I'm having is I'm not 100% sure what it is actually asking for, and how to go about it. The more common proofs involving two variable functions and a given limit are easy enough to do, but I'm stuck on this one. 2. Relevant equations Suppose [itex] f: \left( \mathbb R ^2 , \| . \|_2 \right) \rightarrow \left( \mathbb R , | .| \right) [/itex] is continuous at [itex] \left(a,b \right) \in \mathbb R^2 [/itex]. Prove using the [itex] \epsilon - \delta [/itex] definition only, that if we define the function [itex] f_b : \left( \mathbb R,|.| \right) \rightarrow \left( \mathbb R,|.| \right) [/itex] s.t. [itex] f_b \left(x \right) = f \left( x,b \right), [/itex] then [itex] f_b [/itex] is continuous at [itex] x=a [/itex]. 3. The attempt at a solution Well, considering I am not actually sure what the question is acting for I can't go very far. I was assuming you would set up the usual proof as, Let [itex] \epsilon > 0 [/itex] if [itex] |(x,b) - (a,b)| < \delta [/itex] then [itex] |f(x,b) - (a,b)| < \epsilon [/itex] Possibly then, [itex] x - a < \delta [/itex]? Any help would be appreciated, cheers.