Question

# Find the limit and discuss the continuity of the function. \lim_(x, y, z)\rightarrow (1, 3, 4)\sqrt{(x+y+z)}

Limits and continuity
Find the limit and discuss the continuity of the function. $$\displaystyle\lim_{{{x},{y},{z}}}\rightarrow{\left({1},{3},{4}\right)}\sqrt{{{\left({x}+{y}+{z}\right)}}}$$
substituting (1,3,4) into the function, and the limit is $$\displaystyle{2}\sqrt{{{2}}}$$
function is continuous in the region $$\displaystyle{x}+{y}+{z}\geq{0}$$