calculate the following limit. lim 1-cos(3t)/t as t approahces to 0

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calculate the following limit. lim 1-cos(3t)/t as t approahces to 0

Mathematics
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using LeHopital Rule ==> lim 3sin(3t) = 0
left hand side is infinity, right hand it negative infinity
i don't get it.

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http://www.wolframalpha.com/input/?i=lim+1-cos%283t%29%2Ft+as+t+approaches+to+0+
i tried that site but i want mathematic process. not the graph one.
that was a little while for me to tell you mathematically, but i know if you look at the graph and imagine when t get close to zero, you'll is it gets to a very small number or a big number. it depends which way you look it it

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