Question

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

Answer 1

The given function is f (x)=xn
It is evident that f is defined at all positive integers,n,and its value at n is nn.

Then, $\lim\limits_{x \to n}$ f(n) = $\lim\limits_{x \to n}$ f(xn) = nn
∴$\lim\limits_{x \to n}$ f(x) = f(n)

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