# 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}

Find the limit (if it exists) and discuss the continuity of the function.
$\underset{\left(x,y,z\right)\to \left(-3,1,2\right)}{lim}\frac{\mathrm{ln}z}{xy-z}$

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comentezq
Everything is defined at the given point, so we can just directly substitute.
$\underset{\left(x,y,z\right)\to \left(-3,1,2\right)}{lim}\frac{\mathrm{ln}z}{xy-z}=\frac{\mathrm{ln}2}{-3\left(1\right)-2}=-\frac{\mathrm{ln}2}{5}$
The function is continuous at this point and where $xy\ne qz$