Is the sequence divergent or convergent?

#lim n→∞ [(6n^3 + sin(11n)^2)/(n^2 +10)]#

1 Answer
Mar 18, 2018

Answer:

See below.

Explanation:

#(6n^3)/(n^2 +10) le (6n^3 + sin(11n)^2)/(n^2 +10) #

and

#(6n^3)/(n^2 +10) = (6n)/(1+10/n)#

and

#lim_(n->oo)(6n)/(1+10/n) = oo#

hence

#lim_( n→∞) [(6n^3 + sin(11n)^2)/(n^2 +10)]# diverges