## Related questions with answers

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

VerifiedSolution A

Solution B

Answered 1 year ago

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.

Answered 1 year ago

Step 1

1 of 3$f\left(x,y \right)=\ln\left( 1-x^{2}-y^{2}\right)$

The function $g\left(x,y \right)= 1-x^{2}-y^{2}$ being a polynomail,is conctinuous for all $\left( x,y\right)$ also $f\left( t\right)=\ln\left(t \right)$ is continuous for every real number $t\succ 0$:

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