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SOLVED:A caution about centered difference quotients (Contimuation of Exercise 65 . ) The quotient (f(x h)-f(x-h))/(2 h) may have a limit as h →0 when f has no derivative at x . As a case in point, take f(x)=|x| and calculate limh →0 (|0 h|-|0-h|)/(2 h). As you will see, the limit exists even though f(x)=|x| has no derivative at x=0 . Moral: Before using a centered difference quotient, be sure the derivative exists.
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