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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.$$f(x, y)=\sin ^{-1}(y-x)$$

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(a) The domain is $D=\{(x, y) |-1 \leq y-x \leq 1\}$(b) Range of the given function is [-1,1](c) The level curves are straight lines with slope 1 and $y$ -intercepts belong to the set [-1,1](d) The boundary of the domain is $B=\{(x, y) | y=x \pm 1\}$(e) Domain is closed because it contains ALL its boundary points.(f) unbounded

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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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01:30

(A) find the function'…

(a) find the function'…

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02:43

In Exercise (a) find the f…

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