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.

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.