Question

# Find the limit and discuss the continuity of the function. lim_(x, y)→(0, 1) arccos(x/y) / 1+xy

Limits and continuity
Find the limit and discuss the continuity of the function. $$\displaystyle\lim_{{{x},{y}}}→{\left({0},{1}\right)}\frac{{\arccos{{\left(\frac{{x}}{{y}}\right)}}}}{{1}}+{x}{y}$$
Substituting (0,1) into the function, and the limit is $$\displaystyle{\frac{{\pi}}{{{2}}}}$$ funcion is continuous in the region $$\displaystyle{x}{y}\ne{q}{1},{\left|{\frac{{{x}}}{{{y}}}}\right|}\leq{\frac{{\pi}}{{{2}}}}$$, that's when the denominator is not zero and arccos is defined.