Using the -definition of a limit of a sequence, show that the sequence {xn} diverges and find its limit. xn = (n^2 +3) / n

Using the ε-definition of a limit of a sequence, show that the sequence {xn} diverges and find its limit.

xn = (n^2 +3) / n

Hint: The ε-definition of a divergent sequence: A sequence {xn} diverges if, for every x ∈ R, there exists ε0 > 0 such that for every M ∈ N there is some n ≥ M such that |xn − x| ≥ ε0. For a specific value of ε0, we can take, for example, ε0 = 1.