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?
2 Answers
Kindly refer to the Explanation.
Explanation:
To show that
continuity at
We know that,
As
Similarly,
Finally,
See below:
Explanation:
For a function to be continuous at a point (call it 'c'), the following must be true:

#f(c)# must exist. 
#lim_(x>c)f(x)# must exist
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 :)