Problem 303 (difficulty: 4/10)

Calculate the limit of the following sequences.

    (1)  \(\displaystyle \frac{6n^4+2n^2\cdot (-1)^n}{n^4}\),      (2)  \(\displaystyle \sqrt{n^2 +2} +\sqrt{n^2 -2} -2n;\)
    (3)  \(\displaystyle \frac{\sqrt[n]{n^n-5^n}}{n}\),      (4)  \(\displaystyle n\cdot(\sqrt {n^2+n} -\sqrt {n^2-n})\).

Give me another random problem!