Question

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

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

2021-02-10

Given: $$\lim_{(x,y)\rightarrow(1,0)}\frac{\sin xy}{xy}$$
for finding this limit we first substitute $$x=1$$, then use limit of y
so,
$$\lim_{(x,y)\rightarrow(1,0)}\frac{\sin xy}{xy}=\lim_{y\rightarrow0}\frac{\sin(1)y}{(1)y}$$
$$=\lim_{y\rightarrow0}\frac{\sin y}{y}$$
$$=1$$
hence, given limit is equal to 1.