Q. 43.7( 104 Votes )

# Prove that the function f (x) = x^{n} is continuous at x = n, where n is a positive integer.

Answer :

It is given that function f (x) = x^{n}

We can see that f is defined at all positive integers, n and the value of f at n is n^{n}.

= n^{n}

Thus,

Therefore, f is continuous at x =n, where n is a positive integer.

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