SOLUTION: find the limit as n-infinity (a) sin(n)-n divided by n cube

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Question 290239: find the limit as n-infinity
(a) sin(n)-n divided by n cube
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28n%29=%28sin%28n%29-n%29%2Fn%5E3
f%28n%29=sin%28n%29%2Fn%5E3-1%2Fn%5E2
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The sine function varies from [-1,1]
lim%28+n-%3Einfinity%2C+%28sin%28n%29%2Fn%5E3%29+%29=0
lim%28+n-%3Einfinity%2C+%281%2Fn%5E2%29+%29=0
So then
lim%28+n-%3Einfinity%2C+%28%28sin%28n%29-n%29%2Fn%5E3%29+%29=0