Question

# In given problem, describe the largest set S on which it is correct to say that f is continuous.$f(x, y)=\ln \left(1-x^2-y^2\right)$

Solutions

Verified

The given function is continuous for every $(x,y)$ for which the natural logarithm is defined.

$\ln{(t)}$ is defined for every real positive value $t$. In this case, in order for $t$ to be positive, the pair $(x,y)$ must satisfy:

$x^2+y^2<1$

Therefore, the given function $f$ is continouos inside an origin centered circle with the radius of 1.

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