Question

Prove that x^n is continuous at x=n, where n is positive integer?

Answer 1

See Below...

Explanation:

The given function is `f(x) = x^n`

We can see that, this function is defined for any number `a in R`, where the value would be `a^n`.

So, `lim_(xrarrn^+) f(x) = lim _(xrarrn^-) f(x) = n^n`

and `f(n) = n^n`

Hence Proved.