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.

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is his Solution of Problem 2011-23.