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Unformatted text preview: The derivative of f at x is given by provided the limit exists. x x f x x f x f x  + = ) ( ) ( lim ) ( ' Notation for Derivatives Notation for Derivatives ) ( ' x f dx dy ' y [ ] ) ( x f dx d [ ] y D x Alternative form of the Alternative form of the Derivative Derivative c x c f x f c f c x= ) ( ) ( lim ) ( ' Thm. 2.1 Differentiability Thm. 2.1 Differentiability Implies Continuity Implies Continuity If f is differentiable at x = c, then f is continuous at x = c. It is possible for a function to be continuous at x = c and not be differentiable at x = c. Thus, continuity does not imply differentiability. Joke Time Joke Time What would America be called if we all drove pink cars? A pink carnation! Why should you never play cards in the jungle? Its full of cheetahs!...
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 Fall '08
 JARVIS
 Calculus, Derivative, Slope

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