vinay.singh84 0 Report post Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = (1-1/e) How would one derive this limit? Quote Share this post Link to post Share on other sites
0 Rob_Gandy 2 Report post Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = 1 not (1-1/e) Quote Share this post Link to post Share on other sites
0 k-man 26 Report post Posted November 27, 2012 The limit is neither 1 nor 1-1/e. It's 1/e. Quote Share this post Link to post Share on other sites
0 vinay.singh84 0 Report post 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 Share this post Link to post Share on other sites
0 nitinjain92 0 Report post 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 + 1/2x^{2} + 1/3x^{3} ..... 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 Share this post Link to post Share on other sites
lim((1-1/x)^x) [x→ ∞] = (1-1/e)
How would one derive this limit?
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