So I'm having trouble writing a formal (and complete) proof in Multi-variable calculus. For example, there is the following question:
Show that $$\lim_{(x, y) \to (1, 1)} (x+y) = 2.$$
I know that we will proceed, like we did in one-variable calculus, by finding an appropriate value for $\delta$ in terms of $\epsilon$ by doing some scratch work and then plugging it in in order to end up with the $\mid f(x)-L\mid < \epsilon$. Thereby ending the proof.
Can someone please construct a formal and complete proof as to how this will be tackled step-by-step so that I may be able to learn proving in multi-variable calculus? It will be much appreciated.
$|(x+y)-2|=|x-1+y-1| \le |x-1|+|y-1|$
Your turn !