Engineering Calculus Notes 274

Engineering calculus notes 274

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Unformatted text preview: 262 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION We will exploit this equation in two ways. For notational convenience, we will drop reference to where a partial is being taken: for the rest of this proof, ∂f ∂f = (x, y ) ∂x ∂x ∂f ∂f = (x, y ) ∂y ∂y → where − = (x, y ) is the point at which we are trying to prove x differentiability of φ. Moving the first two terms to the left side, dividing by (△x)( ∂f ), and ∂y taking absolute values, we have △y ∂f /∂x +...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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