Is the sequence divergent or convergent?

Question

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

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Answer 1 · 2018-03-18T20:09:39

See below.

#(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