Question

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

Answer 1

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.