Wednesday, 13 May 2015

derivatives - Confusion in understanding continuous function

Okay so I've started to study derivatives and there is this idea of continuity. The book says "a real valued function is considered continuous at a point iff the graph of a function has no break at the point of consideration, which is so iff the values of the function at the neighbouring points are close enough to the value of the the function at the given point"




So what I dont understand is that why is it that values of the function at the neighbouring points should be close enough to the value of the function at the given point, isn't it enough if they are defined why do they have to be close enough the value of the function at the given point?

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...