Evaluate:       4 44 42 1 1lim2 1 1nn nn n  

To evaluate the given limit, we can start by simplifying the expression inside the parentheses.

First, let's simplify the numerator: 4n^4 - 44n^2 + 42

Next, let's simplify the denominator: n^2 - 1

Now, let's divide both the numerator and the denominator by n^2, since n^2 is the highest power of n in both the numerator and the denominator: (4n^4/n^2) - (44n^2/n^2) + (42/n^2) / (n^2/n^2) - (1/n^2)

Simplifying further, we get: 4 - 44/n^2 + 42/n^2 / 1 - 1/n^2

As n approaches infinity, the terms with 1/n^2 become negligible compared to the other terms. Therefore, we can ignore those terms in the expression.

So, the simplified expression becomes: 4 - 44/n^2 + 42/n^2

Now, as n approaches infinity, both -44/n^2 and 42/n^2 approach 0. Therefore, we can ignore those terms as well.

Finally, we are left with: 4

Therefore, the value of the given limit is 4.