Question

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

Answer 1

`image`

Answer 2

we are given

`\lim_(n \to \infty) (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) ((6n^2+5)/n^2)/((3n^2/n^2))`

`\lim_(n \to \infty) ((6n^2/n^2)+(5/n^2))/((3n^2/n^2))`

now, we can simplify it

`\lim_(n \to \infty) (6+(5/n^2))/(3)`

now, we can plug n=inf

`= (6+(5/(\infty)))/(3)`

`= (6+0)/(3)`

`= (6)/(3)`

`= 2`...............Answer