Continuity at a Point 2

Question

Find the indicated limit, if it exists. 

Answer 1

The function

A function f(x) is continuous at 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

• 

Continuity at a = 2.

f(x) is continuous at 2.

The piecewise function

To find the limit of f(x), when x approaches to 0, 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.