Question

Prove the following limit equals 3 when neN lim[(3n+1)/n] as n → Use the definition of a limit (4.1.2)

Answer 1

Step-by-step explanation:

the function $f(n) = \frac{3n +1 }{n}$  equals 3 only in $x = \infty$ and $x = -\infty$.

Prove:

$\lim\limits_{n \to \pm\infty} \frac{3n +1}{n} = \lim\limits_{n \to \pm\infty} \left(\frac{3n}{n} + \frac{1}{n}\right)$

then

$\lim\limits_{n \to \pm\infty} \left(\frac{3\not{n}}{\not{n}} + \frac{1}{n}\right) = \lim\limits_{n \to \pm\infty} 3 + \frac{1}{n}$

and

$\lim\limits_{n \to \pm\infty} 3 + \not{\frac{1}{n}^0} = 3$