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Evaluate the given functions.$$f(x, y)=x y+x^{2}-y^{2} ; \text { find } f(x, x)-f(x, 0)$$

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Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 1

Functions of Two Variables

Partial Derivatives

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uh huh. We want to evaluate the given functions for F of X, Y and Z X Y plus x squared minus Y squared. We want to evaluate F of X x minus F of X zero. This question is testing our ability to work with multiple functions in particular assessing our knowledge of the fact that to solve, we simply use methods identical single variable functions. That is. We simply plug in the indicated variable. So for instance, if we first find F of X X will plug in extra X X or Y, then we'll do the same for F of X zero. And then we find the difference. So F of X X is simply X times X plus X squared minus X squared or X squared plus X squared plus X squared X squared. Then F of X zero is X +50 plus X squared by the zero squared or x squared. Again, Thus we see there are two evaluated functions of X X and X zero are both X squared. Therefore, we must have that F of X X and F of X zero. Or rather fFS x minus X x zero is experiments X squared equals zero.

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