Use the given graph of $f(x)=\sqrt{x}$ to find a number $\delta$ such that
if $|x-4|<\delta$ then $|\sqrt{x}-2|<0.4$
This precise definition of a limit has been giving me a lot of trouble, but so far I have the left value of x $f(x)=1.6$ $\sqrt{x}=1.6$ $x=2.56$, and the right value $f(x)=2.4$ $\sqrt{x}=2.4$ $x=5.76$
Now, I am stuck because I don't know what to do with this information. I think my main problem is that I don't understand this concept in general. I've been going through my textbook and the problems, I still don't get it. So far I've been able to do questions that already have all of the values of $x$ and $f(x)$ on the graph, but only because I have remembered what steps I'm supposed to take, not that I understand what I'm doing (not even the tiniest bit).
What are my next steps?
Best Answer
Take $\delta=4-2.56$, so each element in the interval $]4-\delta,4+\delta[$ is taken, by $f$, into the $0.4$-neighbourhood of $2$.