# How do you explain why #f(x) = x^2# if #x>=1# and 2x if x<1 is continuous at x = 1?

##### 1 Answer

Nov 30, 2016

It is not continuous at

#### Explanation:

#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