104-hw7 - g ( x ) which is continuous at 0 and so that f (...

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Math 104 - Lecture 1 - Problem Set 7 Due Tuesday, August 3, 2010 Do the following exercises from the book 3.3, 3.5, 3.13. 1. Give a detailed δ - ± proof of the chain rule using the sketch in item (1f) of section 3.1 (page 141). 2. Suppose that f : R R is a differentiable function so that f ( x ) = f ( - x ) (this property is called evenness). Prove that f 0 ( x ) = - f 0 ( - x ). 3. Suppose that f is differentiable at 0 and f (0) = 0. Prove that there is some function
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Unformatted text preview: g ( x ) which is continuous at 0 and so that f ( x ) = xg ( x ). 4. Let f : R R be a dierentiable function so that f is increasing. That is, for x < y , f ( x ) < f ( y ). Prove that any tangent line to f instersects the graph of f exactly once. (For any x , the tangent line at ( x ,f ( x )) is given by the equation f ( x ) ( x-x ) = y-f ( x ).)...
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