Thread: 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?

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

Counter example and

What exactly is the context of this?

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

Originally Posted by transgalactic

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

This is only true if and are of opposite signs... is one example and is another.