Question

Evaluate the limit of lim/n->infinity 6n^2+5/3n^2

Answer 1

we are given

$\lim_{n \to \infty} \frac{6n^2+5}{3n^2}$

we can see that

degree of numerator = degree of denominator =2

so, we can divide both numerator and denominator by n^2

and we get

$\lim_{n \to \infty} \frac{(6n^2+5)/n^2}{(3n^2/n^2)}$

$\lim_{n \to \infty} \frac{(6n^2/n^2)+(5/n^2)}{(3n^2/n^2)}$

now, we can simplify it

$\lim_{n \to \infty} \frac{6+(5/n^2)}{3}$

now, we can plug n=inf

$= \frac{6+(5/(\infty))}{3}$

$= \frac{6+0}{3}$

$= \frac{6}{3}$

$= 2$...............Answer

Answer 2

$\displaystyle \lim_{n\to \infty} \dfrac{6n^2+5}{3n^2 }=\\\\ \lim_{n\to \infty} \dfrac{n^2\left(6+\dfrac{5}{n^2}\right)}{3n^2 }=\\\\ \lim_{n\to \infty} \dfrac{6+\dfrac{5}{n^2}}{3}=\\\\ \dfrac{6+0}{3}=2$