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# Limit derivation

4 replies to this topic

### #1 vinay.singh84

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Posted 27 November 2012 - 08:55 PM

lim((1-1/x)^x) [x→ ∞] = (1-1/e)

How would one derive this limit?
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### #2 Rob_Gandy

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Posted 27 November 2012 - 09:03 PM

Spoiler for I would think

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### #3 k-man

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Posted 27 November 2012 - 10:18 PM

Spoiler for it's neither

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### #4 vinay.singh84

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Posted 28 November 2012 - 12:48 AM

Sorry messed up the OP.
lim(1-(1-1/x)^x) [x→ ∞] = (1-1/e) or lim((1-1/x)^x) [x→ ∞] = 1/e

The main question of how it is derived stlil stands.
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### #5 nitinjain92

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Posted 28 November 2012 - 11:20 AM

lim x->∞ ( 1 - 1 / X )X

(can be written also as )

= lim x->∞ e( X . log( 1 - 1/X ) )
( expansion of log ( 1 - 1/X) ) is -1*( 1/x + 1/2x2 + 1/3x3 ..... so on)

put this in equation we get

= lim x->∞ e( -X *(1/x + 1/2x^2 + 1/3x^3 ..... so on ) )
=lim x->∞ e( -1 *(1 + 1/2x + 1/3x^2 ..... so on ) )
applying limit we get