# Find the limit and discuss the continuity of the function. \lim_(x, y)\rightarrow (2\pi, 4)\sin \frac{x}{y}

Find the limit and discuss the continuity of the function. $$\lim_{x,y \rightarrow 2\pi,4} \sin \frac{x}{y}$$

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Jaylen Fountain

substituting $$\displaystyle{\left({2}\pi,{4}\right)}$$ into the function, and the limit is 1
function is continuous in the region $$y_0< |y|$$, that’s when the denominator is not zero and sin is defined.