1. ## understanding continuety proof..

suppose e>0 b>0

so if
|x-a|<b >>> |x-a|<|x|<b
|f(x)-f(a)|<e >>> |f(x)-f(a)|<|f(x)|<e

from that step they do write same things all over again and conclude that.

lim (f(x))=f(a)
x->infinity

how to get from the step i showed to this conclution?

2. Originally Posted by transgalactic
suppose e>0 b>0

so if
|x-a|<b >>> |x-a|<|x|<b
|f(x)-f(a)|<e >>> |f(x)-f(a)|<|f(x)|<e

from that step they do write same things all over again and conclude that.

lim (f(x))=f(a)
x->infinity

how to get from the step i showed to this conclution?
There must be something missing from your hypothesis.

Why does $\displaystyle |x-a|<b\implies|x|<b$

Counter example $\displaystyle x=1$ and $\displaystyle a=50$

What exactly is the context of this?

3. i ment that if
|x|<b
then this is definitely true
|x-a|<b

4. Originally Posted by transgalactic
i ment that if
|x|<b
then this is definitely true
|x-a|<b
This is only true if $\displaystyle x$ and $\displaystyle a$ are of opposite signs...$\displaystyle x=3,a=-1,b=4$ is one example and $\displaystyle x=-3,a=1,b=4$ is another.