How do you explain why #f(x) = x^2# if #x>=1# and 2x if x<1 is continuous at x = 1?
It is not continuous at
#lim_(xrarr1)f(x) = f(1)#. #" "#(existence of both is implied)
We see from the definition of
In finding the limit, we'll need to consider the left and right limits separately because the rule changes at
The limit from the right is
The limit from the left is
Because the right and left limits are not the same, the limit does not exist.
Therefore the function is not continuous at