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Question
Prove that the function `f(x) = x^n` is continuous at x = n, where n is a positive integer.
Solution
f(x) = xn
`lim_(x->n)` f(x) = `lim_(x -> n)` xn = nn
f(n) = nn
`lim_(x -> n)` f(x) = f(n)
f is continuous at x = n. Where n is a positive integer.
⇒ f is continuous at n ∈ N
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