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N[] MachinePrecision vs. Arbitrary Precision

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  N[] MachinePrecision vs. Arbitrary Precision Rafael Dunn <worthless.trash.junk@gmail.com> - 2011-04-27 09:39 +0000

#1905 — N[] MachinePrecision vs. Arbitrary Precision

Mathematica 8.0.1.0, Mac OSX x86

In:=
N[Sin[Exp[100]]]
N[Sin[Exp[100]], 1]
N[Sin[Exp[100]], 11]

Out:=
-0.999105
0.1
0.14219812366

I realize that N[exp] = N[exp, MachinePrecision].  This indicates when 
N[] is asked to calculate to MachinePrecision, it produces an incorrect 
result in this example.  However, when I use N[exp,n] where n < 
MachinePrecision, I get a correct output.  Is this because N[exp,n] uses 
ExtraPrecision, while N[exp] does not?  If I set MaxExtraPrecision =
0, then N[exp,n] produces a result of 0 with the note that there are no 
significant digits to display until I have made n high enough for 
Mathematica to be able to internally compute it. 

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