sn7_1 - Math 2433 Week 7 Popper007 1. Have you signed up...

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Math 2433 – Week 7 Popper007 1. Have you signed up for a time for your midterm yet? a. YES b. NO (then go do it NOW and come back and choose A) 2. Calculate the partial derivatives. a) b) c) d) e) 15.1 - DIFFERENTIABILITY AND GRADIENT We say that f is differentiable at x if there exists a vector y such that f ( x + h ) ± f ( x ) = y i h + o ( h ). We will say that g ( h ) is o ( h ) if 0 (h) lim 0 h h g = Example: For 2 ( , ) 3 f x y x y = + :
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Let f be differentiable at x . The gradient of f at x is the unique vector f ( x ) such that f ( x + h ) - f ( x ) = f ( x ) i h + o ( h ). Continuing the previous example: More examples:
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Popper007 3. Find the gradient. a) b) c) d) e)
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15.2 Gradients and Directional Derivatives Properties of gradients: Directional Derivatives: Note that u f gives the rate of change of f in the direction of u . And
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1. Find the directional derivative at the point P in the direction indicated. 2
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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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sn7_1 - Math 2433 Week 7 Popper007 1. Have you signed up...

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