3: When n grows to infinity, the "−1" part becomes negligible and we can ignore it. The sine part oscillates, but it is never more than 1 in absolute value, and so it is also eventually dominated by the exponential. Thus one would guess that

To prove this result, the best bet would be the Squeeze theorem (see the box "comparison and oscillation").

Note that our intuitive work showed that the limit is of the type "infinity over infinity". As a such it can be also approached using the l'Hospital rule. However, try it and you will see that here this rule does not help. Why? The usefulness of this rule is that it "removes" terms from the limit. However, we know that exponential and sine/cosine do not disappear when differentiated.

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