`(lim)_(x->0)[((1+x)^(1//x))/e]^(1//x)\ \ `

lim_(x rarr0)(1+x)^((1)/(x))=e

lim_(xto0)((e^(x)-1)/x)^(1//x)

lim_(xto0)((e^(x)-1)/x)^(1//x)

underset( x rarr 0 ) ("Lim") [ ((1+x)^(1//x))/( e ) ]^(1//x)

Let f(x)=g(x)(e^(1//x) -e^(-1//x))/(e^(1//x) + e^(-1//x)) , where g is a continuous function then lim_(x to 0) f(x) exist if

lim_(x rarr0)[((1+x)^((1)/(x)))/(e)]^((1)/(x))

if {x} represents the fractional part of x the value of lim_(x rarr0)[((1+{x})^((1)/(x)))/(e)]^((1)/({x})) is

lim_(x rarr0)(e^(1/x)-e^(-1/x))/(e^(1/x)+e^(-1/x))

lim_(x->0) ((1+x)^(1/x)-e)/x is equal to