substituting (1,3,4) into the function, and the limit is \(\displaystyle{2}\sqrt{{{2}}}\)

function is continuous in the region \(\displaystyle{x}+{y}+{z}\geq{0}\)

function is continuous in the region \(\displaystyle{x}+{y}+{z}\geq{0}\)

Question

asked 2021-06-28

Find the limit (if it exists) and discuss the continuity of the function. \(\displaystyle\lim_{{{x},{y}}}\rightarrow{\left({1},{1}\right)}{\frac{{{x}{y}}}{{{x}²+{y}²}}}\)

asked 2021-05-31

Find the limit and discuss the continuity of the function. \(\displaystyle\lim_{{{x},{y}}}\rightarrow{\left(-{1},{2}\right)}{\frac{{{\left({x}+{y}\right)}}}{{{\left({x}-{y}\right)}}}}\)

asked 2021-05-01

\(\lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-z}\)

asked 2021-05-16

Find the limit (if it exists) and discuss the continuity of the function. \(\displaystyle\lim_{{{\left({x},{y}\right)}→{\left({0},{0}\right)}}}{\frac{{{y}+{x}{e}^{{-{y}²}}}}{{{1}+{x}²}}}\)