# Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(1,0)}frac{sin xy}{xy}

Use the method of your choice to evaluate the following limits.
$\underset{\left(x,y\right)\to \left(1,0\right)}{lim}\frac{\mathrm{sin}xy}{xy}$
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sovienesY

Given: $\underset{\left(x,y\right)\to \left(1,0\right)}{lim}\frac{\mathrm{sin}xy}{xy}$
for finding this limit we first substitute $x=1$, then use limit of y
so,
$\underset{\left(x,y\right)\to \left(1,0\right)}{lim}\frac{\mathrm{sin}xy}{xy}=\underset{y\to 0}{lim}\frac{\mathrm{sin}\left(1\right)y}{\left(1\right)y}$
$=\underset{y\to 0}{lim}\frac{\mathrm{sin}y}{y}$
$=1$
hence, given limit is equal to 1.

Jeffrey Jordon