Question

In given problem, describe the largest set S on which it is correct to say that f is continuous.

f(x,y)=ln(1x2y2)f(x, y)=\ln \left(1-x^2-y^2\right)

Solutions

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Answered 1 year ago

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

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

x2+y2<1x^2+y^2<1

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

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