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
ANSWERED
asked 2021-02-09
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,0)}\frac{\sin xy}{xy}\)

Answers (1)

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.

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