Limit with factorial

It's hard to believe you are serious. Have you done anything on this yourself? Have you tried, for example, calculating values for, say, x= 10, 1000, etc.?

 

I studied the limit but not this type

this question is older than me :)

 

Just a few things that should have made this limit quite obvious -

[tex]n! < n^n, n > 2[/tex]

[tex]n^2 > n[/tex]

Perhaps you have seen how to evaluate the common [tex]\lim_{n\to \infty} n^{\frac{1}{n}}[/tex]?