# Help on continuity

• December 16th 2006, 03:51 AM
Help on continuity
Determine the number at which the function is discontinuous, and show why definition 1.8.1 isnt satisfied at this number
Def 1.8.1
1.) $f(a)$ exists
2.) $\lim_{x \to a}$ exists
3.) $\lim_{x \to a} = f(a)$

$12.)H(x) =$
$6 + x$if $x \leq -2$
$2 - x$if $-2 < x \leq 2$
$2x - 1$if $2 < x$

sorry and thanks very much for your help
• December 16th 2006, 01:47 PM
ThePerfectHacker
Quote:

$12.)H(x) =$
$6 + x$if $x \leq -2$
$2 - x$if $-2 < x \leq 2$
$2x - 1$if $2 < x$

The only possible points are $x=-2,2$
Check $x=-2$.

$\lim_{x\to -2}H(x)$ what is it?
When we approach from the right and from the left we have respectively,
$6+(-2)=4$
$2-(-2)=4$.
Continous!

$\lim_{x\to 2}H(x)$ what is it?
When we appraoch from the right and from the left we have respectively,
$2-(2)=0$
$2(2)-1=3$
Thus it is discontinous.