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

Question
Limits and continuity
Evaluate the following limits.
$$\lim_{(x,y)\rightarrow(0,\pi)}\frac{\cos xy+\sin xy}{2y}$$

2021-02-26
Given,
$$\lim_{(x,y)\rightarrow(0,\pi)}\frac{\cos xy+\sin xy}{2y}$$
By applying the limit, we get
$$\lim_{(x,y)\rightarrow(0,\pi)}\frac{\cos xy+\sin xy}{2y}=\frac{\cos(0\cdot\pi)+\sin(0\cdot\pi)}{2\pi}$$
$$=\frac{\cos(0)+\sin(0)}{2\pi}$$
$$=\frac{1+0}{2\pi}$$
$$=\frac{1}{2\pi}$$

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