# Continuity of Multivariable functions – A quotient of functions with sin – Exercise 4204

Exercise

Is the function

$$f(x,y) = \begin{cases} \frac{(x-1){(y-2)}^2}{{(x-1)}^2+\sin^2(y-2)}, &\quad (x,y) \not= (1,2)\\ 0, &\quad (x,y)= (1,2)\\ \end{cases}$$

Continuous at point (1,2)?