1

Is $f:[0, \infty) \rightarrow \mathbb{R}$ $f(x)=[x^{1/2}]$ continuous at 0?

My Attempt

Now using the limit method, and as the function is only defined on $[0, \infty)$ $$\lim_{x \to +0}=\lim_{x \to 0}=0=f(0)$$ and so $f(x)$ is continuous at 0.

I know its a simple question but is this method correct, or is the epsilon-delta method required?

user148713
  • 377
  • 2
    If you want a real proof, you have to show that the limit actually equals to zero via using epsilon-delta definition. – ThePortakal May 20 '14 at 10:54
  • but does this suffice to answer the question, say if it came up in an exam as a simple 2/3 marker – user148713 May 20 '14 at 10:55
  • Your proof consists of true statements. Whether you need something more elementary or not depends on the context and audience (see this answer of mine). Considering the kind of example it is, I'd say this is sufficient because the point of this problem is to deal with the floor function, in my opinion. – Git Gud May 20 '14 at 10:56
  • Yes. Show that the limit from right equals to zero. And since $f(0)=0$ the functionis continuous at zero. – ThePortakal May 20 '14 at 10:57

0 Answers0