continuity at a point 1

Question

Find the indicated limit, if it exists. 

Answer 1

.

To find the limit of f(x), when x approaches to - 1, 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 be the same.So, the limit of the function f(x) is exists, where x approaches - 1

The fact that f(- 1) = 5 has the value of the limit as x approaches - 1.

Therefore, .

Answer 2

A function f(x) is continuous at a point a, if the following three cinditions valid.

• The function is defined at a.That is a is in the domain of definition of f(x).

• is exist

• .

The function f is defined at x = 1, since

The limit

(i). f(1) = 1 + 6 = 7.

(ii). .

(iii). and ,

Therefore, .

So, the three conditions are satisfied and the function is continues at the point 1.

.

To find the limit of f(x), when x approaches to - 1, 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 be the same.So, the limit of the function f(x) is exists, where x approaches - 1

The fact that f(- 1) = 5 has the value of the limit as x approaches - 1.

Therefore, .

.

To find the limit of f(x), when x approaches to - 1, 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 be the same.So, the limit of the function f(x) is exists, where x approaches - 1

The fact that f(- 1) = 5 has the value of the limit as x approaches - 1.

Therefore, .