Show that the sequence 3n+sin2n6nn∈N is bounded.
I know that 0≤sin2n≤1, so 3n6n=12≤3n+sin2n6n≤3n+16n
So it is easy to see that it is bounded below by 12, but I can't figure out how to show it is bounded above.
How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...
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