Find the limit lim_"n→ oo" cosn^3/(2n)- (3n)/(6n+1)?

lim_"n→ oo" cosn^3/(2n)- (3n)/(6n+1)

1 Answer
Mar 13, 2018

lim_(n->oo) cos(n^3)/(2n) - (3n)/(6n+1) =-1/2

Explanation:

The limits of both addends are finite, and we can evaluate them separately:

lim_(n->oo) cos(n^3)/(2n) = 0

as abs(cos(n^3)) <=1, so the numerator is bounded and the denominator tends to +oo.

lim_(n->oo) (3n)/(6n+1) = lim_(n->oo) 3/(6+1/n) = 3/6 = 1/2

Then:

lim_(n->oo) cos(n^3)/(2n) - (3n)/(6n+1) = 0-1/2 = -1/2