Question

12.The function f(x,y)=x+y is
continuous for​

Answer 1

Answer:

The function f(x,y)=x is continuous since given ϵ>0 and (a,b)∈R2, setting δ=ϵ makes

|f(x,y)−f(a,b)|=|x−a|=(x−a)2−−−−−−−√≤(x−a)2+(y−b)2−−−−−−−−−−−−−−−√<ϵ

whenever (x−a)2+(y−b)2−−−−−−−−−−−−−−−√<δ. Similarly, the function g(x,y)=y is continuous.