Question

Prove that the function is continuous at x = n , where n is a positive integer.

Answer 1

The given function is,

f( x )= x n

At x=n, the function becomes,

f( n )= n n

The left hand limit of the function at x=n is,

LHL= lim x→n f( x ) = lim x→n ( x n ) = n n

The right hand limit of the function at x=n is,

RHL= lim x→n f( x ) = lim x→n ( x n ) = n n

Therefore, the function is continuous at x=n, where n is positive integer.