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Math Help - Analysis in Rn

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    Analysis in Rn

    I have tried to solve this question and I dont find a solution. Can you please help me? Thanks. ( I dont know how to display the problem in latex)

    \noindent a-) Suppose $f: U \to \rr$ where $U$ is an open convex subset of $\rr^n$ and that $(\partial f/ \partial x_1)(p) = 0$ for all $p \in U$. Prove that $f$ depends only on $x_2, x_3, \ldots, x_n$ \\
    \noindent b-) Consider the region $U = \rr^2 \setminus L$ where $L$ is the half-line $\{(x, y): x = 0 \text{ and } y \ge 0\}$. Find a funciton $f: U \to \rr$ such that $(\partial f / \partial x)(p) = 0$ for all $p \in U$ but it is not true that $f$ depends only on $y$.
    Last edited by SpanishTeacher; April 22nd 2013 at 06:04 PM.
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