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Unformatted text preview: < < < < 2. {( , ) : 2 5, 4 6} x y x y 3. {( , ) : 2 5, 4 6} x y x y < < 14.6  Limits and Continuity; Equality of Mixed Partials Do all paths yield the same limit???? Example: Find ( , ) (0,0) lim ( , ) x y f x y for 2 2 2 ( , ) y f x y x y = + Higher order derivatives: What does this mean? Example: In the case of a function of three variables you can look for three first partials , , x y z f f f and there are NINE second partials: , , , , , , , , xy yx xz zx yz zy xx yy zz f f f f f f f f f Example: More examples: Popper006 4. Calculate the secondorder partial derivatives. a) , , b) , , c) , , d) , , e) , , 5. Calculate yz f . a) 2 z yz f e = b) 2 z yz f ye = c) 4 z yz f e = d) 2 x yz f e = e) 3 y yz f xe = 6. B...
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This note was uploaded on 07/20/2010 for the course MATH 18427 taught by Professor Etgen during the Fall '10 term at University of Houston.
 Fall '10
 Etgen

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