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Aug13-06, 12:16 AM
Sci Advisor
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mathwonk's Avatar
P: 9,470
Epsilon-Delta Limit Proof

what are the rest of your decimals? unlkess you tell us exactly what number e is, you cannot prove that e^x really approaches e as x goes to 1 by your method. and unless you define precisely what e^x means you also cannot do it.

the easiest way is halls second method that e^x is continuous, since it is the inverse of the continuous function ln(x), hence it suffices to show e^1 = e, but that follows from the fact that e is defined as the unique number such that ln(e) = 1.