Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have some problem to understand the definition of a continuous function in a point.

I have $f(x) = \sqrt{x}$ and I want to check the continuity of the function above in the point $x_0 = 0$ or for all the $x_0 \ge 0$.

Using the relation between $|f(x) -f(x_0)|< \epsilon$ and $|x - x_0| < \delta$ that states: $\forall\epsilon \in \Bbb R, \exists\delta\in\Bbb R : \forall x \in domain \mathcal (f): |x-x_0| < \delta \Rightarrow |f(x)-f(x_0)| < \epsilon$, how can I check continuity at a point?

Thanks

share|improve this question
add comment

1 Answer

$|f(x) - f(c)| = |\sqrt{x} - \sqrt{c}| \leq\sqrt{|x-c|}$ this shows the continuity of $\sqrt{x}$

share|improve this answer
    
how should I see the continuity from that? –  l_core Nov 5 '12 at 16:24
1  
if |f(x)-f(c)|< epsilon then your delta will be epsilon^2 –  jim Nov 5 '12 at 16:29
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.