Infinity Limit Problem

[Jason76]

Exactly what is going on here?

\(\displaystyle \lim x \rightarrow \infty[\dfrac{n^{1 - \frac{1}{n}}}{2^{\frac{3}{n} + 1}}]\)

If it's too hard to read then the exponents are

\(\displaystyle 1 - \dfrac{1}{n}\) (in big numerator)and \(\displaystyle \dfrac{3}{n} + 1\) (in big denominator)

 

[Jason76]

Corrected notation

Exactly what is going on here?

\(\displaystyle \lim n \rightarrow \infty[\dfrac{n^{1 - \frac{1}{n}}}{2^{\frac{3}{n} + 1}}]\)

If it's too hard to read then the exponents are:

\(\displaystyle 1 - \dfrac{1}{n}\) (in big numerator)and \(\displaystyle \dfrac{3}{n} + 1\) (in big denominator)

Now moving on

The denominator evaluates to \(\displaystyle \infty^{1}\)

But what exactly is going on with the denominator

It seems to be evaluating to \(\displaystyle 2^{1}\)

In that case it would be \(\displaystyle \dfrac{\infty}{2} = \infty\) Is that correct?