# Find the limit (if it exists) and discuss the continuity of the function. \lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-

Find the limit (if it exists) and discuss the continuity of the function.
$$\lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-z}$$

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pivonie8
Everything is defined at the given point, so we can just directly substitute.
$$\displaystyle\lim_{{{\left({x},{y},{z}\right)}\rightarrow{\left(-{3},{1},{2}\right)}}}{\frac{{{\ln{{z}}}}}{{{x}{y}-{z}}}}={\frac{{{\ln{{2}}}}}{{-{3}{\left({1}\right)}-{2}}}}=-{\frac{{{\ln{{2}}}}}{{{5}}}}$$
The function is continuous at this point and where $$\displaystyle{x}{y}\ne{z}$$