❖ Multivariable Calculus: Finding and Sketching the Domain ❖

Multivariable Calculus: Finding and Sketching the Domain of a function z = f(x,y).
In these examples, our domain will be some region D in the XY-plane. To find the region, we approach the problems much like when we have a function of a single variable.
Here I look at two examples of finding the domain and sketching the domain of a multivariable function. In particular we have a function of two variables.

#calculus #domain #multivariablecalculus

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[agingerrail]

Andreajal986, the definition of range is the set of output values that is mapped to by the function after having some input value (the domain). In this case, the domain is the combination of x and y unknowns. Then by inputting it into function f(x, y), you get certain values. These values are the range of the function.

If you want to know some more, when patrick drawn the x, y, z axis system, the range is actually represented by the possible z values outputted from the function, with z = f(x, y).

The definition that range is the y-value only applies if it was a single variable function like f(x) = x^2 + 1, and y = f(x). But as this is multi-variable function, the range is no longer y-value.

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