quiz1 - x = αDf x βDg x 2 Suppose A is open in R 2 and...

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Spring 2006 Math 332 - Real Analysis II Quiz 1, 20/3/2006 1. (MH, page 383, ex.1) Let A be an open subset of R m ; f, g : A R n be differentiable; α, β R . Prove, using the definition, that the function h = αf + βg : A R n is differentiable and for x A , D ( h )(
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Unformatted text preview: x ) = αDf ( x ) + βDg ( x ). 2. Suppose A is open in R 2 and the function f : A → R has partial derivatives on A . Is it true that f is continuous on A ? Ferit ¨ Ozt¨urk, Bo˘gazi¸ci University 2006...
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