Of course you meant .
You have correctly found the left and right hand limits, and they are distinct so, does dot exist the limit as . Hence, has not a continuous extension at .
Fernando Revilla
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 ??
Of course you meant .
You have correctly found the left and right hand limits, and they are distinct so, does dot exist the limit as . Hence, has not a continuous extension at .
Fernando Revilla