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(A) find the function's domain, (b) find the function's range, (c) describe the function's level curves, (d) find the boundary of the function's domain, (e) determine if the domain is an open region, a closed region, or neither, and (f) decide if the domain is bounded or unbounded.$$f(x, y)=\ln \left(9-x^{2}-y^{2}\right)$$

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(a) The domain is $D=\left\{(x, y) | x^{2}+y^{2}<9\right\}$(b) Range of the given function is $(-\infty, \ln (9)]$(c) The level curves are concentric circles with the center at origin and radius less than 3(d) The boundary of the domain is $B=\left\{(x, y) | x^{2}+y^{2}=9\right\}$(e) The domain is open because every point in $D$ is an interior point.(f) bounded

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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(a) find the function'…

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In Exercise (a) find the f…

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