Question

Can someone help me please?
find the limit of (x)/(e^(1/x) +1) for when x->0

Answer 1

\[\lim x->0 for when (\frac{ x }{ e ^{\frac{ 1 }{ x }} +1})\]

Answer 2

the denominator goes to infinity lickety split
the numerator goes to zero

Answer 3

do i need to do any algebra or is it pure speculation?

Answer 4

not sure what algebra you need here
the fact that
\[\lim_{x\to 0}x=0\] is more or less like whose buried in grant's tomb

Answer 5

as for \(e^{\frac{1}{x}}\) that limit is \(\infty\) if \(x\to 0^+\) as \(\lim_{x\to 0^+}\frac{1}{x}=\infty\)

Answer 6

if \(x\to 0^-\) then \(\lim_{x\to 0^-}\frac{1}{x}=-\infty\) and so
\[\lim_{x\to 0^-}e^{\frac{1}{x}}=0\]

Answer 7

oh i get it now.... thanks a bunch :D

Answer 8

yw