sn6_1 - < < < <...

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Math 2433 – Week 6 Popper006 1. Differentiate a) b) c) d) e) 14.4 – Partial Derivatives The partial derivative of f with respect to x is the function fx obtained by differentiating f with respect to x , treating y as a constant. The partial derivative of f with respect to y is the function fy obtained by differentiating f with respect to y , treating x as a constant. Examples: Find the partial derivatives: 1.
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2.
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More examples: Equations of tangent lines Let and let C be the curve of intersection of the surface with the plane y = 2. Find equations for the line tangent to C at the point P (3, 2, 3).
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Popper006 2. Calculate the partial derivatives. a) b) c) d) e) 3. Find and g iven that a) b) c) d) e)
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14.5 - Open and closed sets Examples: 1. {( , ) : 2 5, 4 6} x y x y
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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 second-order 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.

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sn6_1 - < < < <...

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