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-

Kye 2021-09-23 Answered

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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Expert Answer

pivonie8
Answered 2021-09-24 Author has 6234 answers
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 \(\displaystyle{x}{y}\ne{z}\)
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