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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.$$f(x, y)=\tan ^{-1}\left(\frac{y}{x}\right)$$

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(a) Domain is $D=\{(x, y) | x \neq 0\}$(b) $\quad$ Range of $f(x, y)=\tan ^{-1}\left(\frac{y}{x}\right)$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$(c) The level curves are straight lines passing through the origin.(d) The boundary of the domain is $B=\{(x, y) | x=0\}$(e) The domain is open because every point in $D$ is an interior point.(f) unbounded

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

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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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In Exercise (a) find the f…

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(a) find the function'…

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(A) find the function'…

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