# Evaluate the following limits. lim_{(x,y)rightarrow(0,pi)}frac{cos xy+sin xy}{2y}

Evaluate the following limits.
$\underset{\left(x,y\right)\to \left(0,\pi \right)}{lim}\frac{\mathrm{cos}xy+\mathrm{sin}xy}{2y}$
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Asma Vang
Given,
$\underset{\left(x,y\right)\to \left(0,\pi \right)}{lim}\frac{\mathrm{cos}xy+\mathrm{sin}xy}{2y}$
By applying the limit, we get
$\underset{\left(x,y\right)\to \left(0,\pi \right)}{lim}\frac{\mathrm{cos}xy+\mathrm{sin}xy}{2y}=\frac{\mathrm{cos}\left(0\cdot \pi \right)+\mathrm{sin}\left(0\cdot \pi \right)}{2\pi }$
$=\frac{\mathrm{cos}\left(0\right)+\mathrm{sin}\left(0\right)}{2\pi }$
$=\frac{1+0}{2\pi }$
$=\frac{1}{2\pi }$
Jeffrey Jordon