Friday, July 12, 2019

calculus - Proving |sinxsiny|<|xy|



From Spivak's Calculus:




Prove that |sinxsiny|<|xy| for all xy. Hint: the same statement, with < replaced by , is a straightforward consequence of a well-known theorem.





Now, I might even be able to prove this somehow (?), but I can't seem to figure out what "well-known theorem" the author is alluding to here... any hints?


Answer



Maybe it's referring to the mean value theorem.


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