Why the function is discontinuous at a=1 given #f(x)= 1-x^2# if x < 1 and #f(x)= 1/x# if #x >= 1#?
1 Answer
The limit as
Explanation:
There are three requirements for a function
(i)
(ii)
(iii)
PART 1 We will check if
PART 2 We will check if
Since the right-hand limit and the left-hand limit are not equal, then the limit as
The second requirement is not true, therefore the function is discontinuous.