Question
Prove that the function $f(x) = {x^n}$ is continuous at x $=$ n, where n is a positive integer
Continuity and Differentiability — Class 12 Maths Solution
Step-by-step Solution
Given, $f(x) = {x^n},n \in N$
So, f (x) is a polynomial function and domain of f is R.
$\mathop {\lim }\limits_{x \to n} f(x) = \mathop {\lim }\limits_{x \to n} {x^n} = {x^n} = f(n)$
Hence it states that f is continuous at n$\in$N.
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