vinay.singh84 Posted November 27, 2012 Report Share Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = (1-1/e) How would one derive this limit? Quote Link to comment Share on other sites More sharing options...
0 Rob_Gandy Posted November 27, 2012 Report Share Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = 1 not (1-1/e) Quote Link to comment Share on other sites More sharing options...
0 k-man Posted November 27, 2012 Report Share Posted November 27, 2012 The limit is neither 1 nor 1-1/e. It's 1/e. Quote Link to comment Share on other sites More sharing options...
0 vinay.singh84 Posted November 27, 2012 Author Report Share Posted November 27, 2012 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. Quote Link to comment Share on other sites More sharing options...
0 nitinjain92 Posted November 28, 2012 Report Share Posted November 28, 2012 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 answer = e -1 Quote Link to comment Share on other sites More sharing options...
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vinay.singh84
lim((1-1/x)^x) [x→ ∞] = (1-1/e)
How would one derive this limit?
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