# Evaluate the following limits. lim_{(x,y)rightarrow(e^2,4)}lnsqrt{xy}

Lennie Carroll 2020-12-30 Answered
Evaluate the following limits. $\underset{\left(x,y\right)\to \left({e}^{2},4\right)}{lim}\mathrm{ln}\sqrt{xy}$
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## Expert Answer

Daphne Broadhurst
Answered 2020-12-31 Author has 109 answers
Given limit expression is $\underset{\left(x,y\right)\to \left({e}^{2},4\right)}{lim}\mathrm{ln}\sqrt{xy}$
Evaluate the limit value.
$\underset{\left(x,y\right)\to \left({e}^{2},4\right)}{lim}\mathrm{ln}\sqrt{xy}=\mathrm{ln}\sqrt{\left({e}^{2}\right)\left(4\right)}$
$=\sqrt{\left(2e{\right)}^{2}}$
$=\mathrm{ln}\left(2e\right)$
$=\mathrm{ln}2+\mathrm{ln}\left(e\right)$
$=\mathrm{ln}2+1$
$\approx 1.69315$
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Jeffrey Jordon
Answered 2022-04-01 Author has 2087 answers

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