Find the limit or explain why it diverges?

Find the limit of sqrt(9n^2-5n+3)/root(4)(16n^4-7n^3+4n+1)

1 Answer
Jul 20, 2017

3/2

Explanation:

sqrt(9n^2-5n+3)/root(4)(16n^4-7n^3+4n+1) = n/n sqrt(9-5/n+3/n^2)/root(4)(16-7/n+4/n^3+1/n^4) = sqrt(9-5/n+3/n^2)/root(4)(16-7/n+4/n^3+1/n^4)

now

lim_(n->oo)sqrt(9n^2-5n+3)/root(4)(16n^4-7n^3+4n+1) =lim_(n->oo)sqrt(9-5/n+3/n^2)/root(4)(16-7/n+4/n^3+1/n^4) =

=(lim_(n->oo)sqrt(9-5/n+3/n^2))/(lim_(n->oo)root(4)(16-7/n+4/n^3+1/n^4)) = sqrt(9)/root(4)(16) = 3/2