# 2011-23 Constant Function

Let $$f:\mathbb{R}^n\to \mathbb{R}^{n-1}$$ be a function such that for each point a in $$\mathbb{R}^n$$, the limit $$\lim_{x\to a} \frac{|f(x)-f(a)|}{|x-a|}$$ exists. Prove that f is a constant function.

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2011-23 Constant Function, 4.8 out of 5 based on 9 ratings