vector3

Vector3 - 3(d Use the definition of directional derivative(in terms of limits or the dot product ∇ f -→ u to find the derivative of this

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Quiz 2 – Math 223 – Due Thursday 9/20/2007 Name: Signature: Hand in these problems worked out. Partial credit is possible, but you must show all work. Let f ( x, y ) = x ( x 2 + y 2 ) 3 / 2 . (a) Use a difference quotient to approximate f x (1 , 3) with h = 0 . 001. 1
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2 (b) Use partial derivatives to find f x (1 , 3). Was the approximation in part (a) reasonable? (c) Use the definition ( a.k.a., limits ) to find f x (1 , 3). Use pure algebraic skills (i.e., no l’Hopital’s rule).
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Unformatted text preview: 3 (d) Use the definition of directional derivative (in terms of limits) or the dot product ∇ f ·-→ u to find the derivative of this function in the direction of-→ v =-→ i-3-→ j , at the point (1,3). Here-→ u is the unit vector in the direction of-→ v . 4 (e) Find the direction of maximal rate of change for the function f ( x, y ) at the point (1,3)....
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This note was uploaded on 09/23/2010 for the course MATH 216 taught by Professor Dickson during the Spring '10 term at UAA.

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Vector3 - 3(d Use the definition of directional derivative(in terms of limits or the dot product ∇ f -→ u to find the derivative of this

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