Continuity at a Point 4

Question

Find the indicated limit, if it exists. 

Answer 1

The function f is defined at x = 4, since

The limit

(i). f(4) = x + 10 = 4 + 10 = 14.

(ii). .

(iii). and ,

Therefore, .

So, the three conditions are satisfied and the function is continues at the point 4.

.

To find the limit of f(x), when x approaches to 8, first find the left hand side limit and then right hand side limit.

The limit exists only, if the two limits i.e, left hand side limit and right hand side limit would be the same.

Means, that,

.

.

The limit would not be the same.

So, the limit of the function f(x) does not exists, where x approaches 8.