# Math Help - Continuous extension at a point

1. ## Continuous extension at a point

I have the function
f(x) = (x^8)\ |x-2|

I have to determine if the function has a continuous extension at x=2 ???

My solution is

1- Lim (x-2)(x^2+2x+4)\(x-2)= 12 if x>or equal to 2
x goes to 2

2- Lim (x-2)(x^2+2x+4)\ - (x-2)= -12 if x less than 2
x goes to 2

Is there a continuous extension at x=2 ??????????????? although we have two values (12, -12) because of (absolute value) ??

or there is not continuous extension ??

2. Originally Posted by mariama
I have the function
f(x) = (x^8)\ |x-2|

Of course you meant $f(x)=(x^3-8)/(|x-2|)$ .

You have correctly found the left and right hand limits, and they are distinct so, does dot exist the limit as $x\to 2$ . Hence, $f$ has not a continuous extension at $x=2$ .

Fernando Revilla