# James

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# 2,330 Reputation

10 Dec 14
 +10 16:43 upvote Coffee Break Riddle
5 Dec 5
 +5 05:50 upvote If $a \frac{\partial}{\partial x} (f+g) = \sin(f-g)$ and $f= f_0 + af_1 + a^2 f_2 + a^3 f_3+…$, then finding $f_0, f_1, f_2$ and $f_3$
21 Nov 29
 +10 17:09 2 events If $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ smooth, $g(x,y)= x^3 + y^3$ and $g \circ f \equiv 0$, then $\det Df \equiv 0$ +5 04:50 upvote If $f: U \rightarrow \mathbb{R}^n$ differentiable such that $|f(x)-f(y)| \geq c |x-y|$ for all $x,y \in U$, then $\det \mathbf{J}_f(x) \neq 0$ +2 18:30 accept If $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ smooth, $g(x,y)= x^3 + y^3$ and $g \circ f \equiv 0$, then $\det Df \equiv 0$ +2 13:36 accept If $f: U \rightarrow \mathbb{R}^n$ differentiable such that $|f(x)-f(y)| \geq c |x-y|$ for all $x,y \in U$, then $\det \mathbf{J}_f(x) \neq 0$ +2 03:04 accept $f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
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