Question
Prove that the function $f(x) = {x^n}$ is continuous at x = n where n is a positive integer.
Continuity at x = n, $\mathop {\lim }\limits_{x \to n} f\left( x \right) = \mathop {\lim }\limits_{x \to n} \left( {{x^n}} \right) = {n^n}$
And $f\left( n \right) = {n^n}$
Since $\mathop {\lim }\limits_{x \to n} f\left( x \right) = f\left( x \right)$, therefore, $f\left( x \right)$ is continuous at x = n.
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