The graph of h(x) is shown. The graph appears to be continuous at , where the definition changes. Show that h is in fact continuous at by finding the left and right limits and showing that the definition of continuity is met?
Kindly refer to the Explanation.
To show that
We know that,
For a function to be continuous at a point (call it 'c'), the following must be true:
The former is defined to be true, but we'll need to verify the latter. How? Well, recall that for a limit to exist, the right and left hand limits must equal the same value. Mathematically:
This is what we'll need to verify:
To the left of
Now, we just evaluate these limits, and check if they're equal:
So, we have verified that
Hope that helped :)