Good day.
Is $\sin(x^{2}+y^{2})-\exp\left(\tan\left(\frac{1}{x^{2}+y^{2}+1{}}\right)\right)$ continuous function in all $\mathbb{R^2}$? Wolfram indicates affirmative, but the points in that the tangent function is undefined?
Thanks.
2026-05-14 21:25:56.1778793956
A continuous function in two variables
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Yes, it is a continuous function, since it was obtaind from continuous functions using composition and arithmetic operations. The fact that it is undefind at certain points is not relevant. The function$$\begin{array}{ccc}\Bbb R\setminus\{0\}&\longrightarrow&\Bbb R\\x&\mapsto&\dfrac1x\end{array}$$is continuous, although it is undefined at $0$.