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

Explanation:

the function
`f(n) = (3n +1 )/(n)` equals 3 only in
`x = \infty` and
`x = -\infty`.

Prove:

`\lim\limits_(n \to \pm\infty) (3n +1)/(n) = \lim\limits_(n \to \pm\infty) \left((3n)/(n) + (1)/(n)\right)`

then

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

and

`\lim\limits_(n \to \pm\infty) 3 + \\ot{(1)/(n)^0} = 3`