Question

\[\lim_{x \rightarrow 0} (\frac{ (1+x)^\frac{ 1 }{ x } }{ e })^\frac{ 1 }{ x }\]

Answer 1

@AravindG
Mr. Admin please give me solution not *answer* !!

Answer 2

@AravindG ?

Answer 3

@hartnn ?? @ganeshie8 ??

Answer 4

@zepdrix ?? @Hero ??

Answer 5

@AravindG ?

Answer 6

@thomaster ?

Answer 7

@beccaboo333 ?? @Luigi0210 ??

Answer 8

let that limit be = L
then take log on both sides and simplify the right side using log rules.

Answer 9

u mean like
log L=\[\frac{ 1 }{ x }(\log \lim_{x \rightarrow 0} (1+x)^\frac{ 1 }{ x }-\log \lim_{x \rightarrow 0} x)\]

Answer 10

@hartnn ?

Answer 11

@hartnn ??

Answer 12

@Hero ?? @ganeshie8 ??

Answer 13

sorry for late replies, my internet connection is very slow,
don't you have a standard result for limit x \(\to 0 \) of log (1+x)^(1/x)
?
if not, which standard limit formulas can you use ?

Answer 14

the simplification i made isnt correct?

Answer 15

can u simplify please!

Answer 16

@hartnn ?

Answer 17

\(\large \ln L = \lim \limits_{x\to0} (1/x) [\ln (1+x)^{(1/x)}-\ln e]\)

Answer 18

lne=1

Answer 19

@hartnn ?? now?

Answer 20

@hartnn ?

Answer 21

@hartnn ?