The question is, find the limit of an=(en+3n)/5n as n→∞
I tried using L'hopital's rule, but didn't seem to get anything useful, so I figured I may be able to use the squeeze theorem. Would this be an appropriate use of the squeeze theorem, and would there be a better method to proving that the limit approaches zero?
1/n≤(en+3n)/5n≤10/n for all n, with both 1/n and 10/n approaching zero as n approaches infinity.
Answer
Hint: I don't believe the bounds you have are correct. Instead, I suggest something like 0≤en+3n5n≤3n+3n5n=2⋅3n5n.
These inequalities are much more obvious, hold for all n, thus we can take the limit. What do we get?
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