Question

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

Limits and continuity
ANSWERED
asked 2021-05-01
Find the limit and discuss the continuity of the function. \(\displaystyle\lim_{{{x},{y}}}→{\left({0},{1}\right)}\frac{{\arccos{{\left(\frac{{x}}{{y}}\right)}}}}{{1}}+{x}{y}\)

Expert Answers (1)

2021-05-02
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.
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