# understanding continuety proof..

• Dec 31st 2008, 02:43 PM
transgalactic
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?
• Dec 31st 2008, 10:49 PM
Mathstud28
Quote:

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?
• Jan 2nd 2009, 02:40 PM
transgalactic
i ment that if
|x|<b
then this is definitely true
|x-a|<b
• Jan 2nd 2009, 06:27 PM
Mathstud28
Quote:

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.