# Evaluate the following limits. lim_{(x,y,z)rightarrow(0,1,0)}ln(1+y)e^{xz}

e1s2kat26 2020-11-08 Answered
Evaluate the following limits.
$\underset{\left(x,y,z\right)\to \left(0,1,0\right)}{lim}\mathrm{ln}\left(1+y\right){e}^{xz}$
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## Expert Answer

Nathanael Webber
Answered 2020-11-09 Author has 117 answers
Consider the following limit:
$\underset{\left(x,y,z\right)\to \left(0,1,0\right)}{lim}\mathrm{ln}\left(1+y\right){e}^{xz}=\mathrm{ln}\left(1+1\right){e}^{0×0}$
$=\mathrm{ln}\left(2\right){e}^{0}$
$=\mathrm{ln}\left(2\right)×1$
$=\mathrm{ln}\left(2\right)$
Hence, the solution is $\underset{\left(x,y,z\right)\to \left(0,1,0\right)}{lim}\mathrm{ln}\left(1+y\right){e}^{xz}=\mathrm{ln}\left(2\right)$
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