Definitions for taper off
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Princeton's WordNet
taper off, peter out, fizzle out, fizzle(verb)
end weakly
"The music just petered out--there was no proper ending"
taper off(verb)
become smaller or less active
"Business tapered off"
Wiktionary
taper off(Verb)
To diminish or lessen gradually; to become smaller, slower, quieter, etc.
Citation
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"taper off." Definitions.net. STANDS4 LLC, 2013. Web. 24 May 2013. <http://www.definitions.net/definition/taper off>.