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# Continuity of Multivariable functions – A quotient of functions with sin – Exercise 4195

Exercise

Is the function

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

Continuous at point (1,2)?