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

lim_(x rarr0)(1+2x)^(5/x)

lim_(x rarr0)(cot^(-1)(1/x))/(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)((1+x)^(4)-1)/(x)

lim_(x rarr0)((1+x)^(4)-1)/(x)

lim_(x rarr0)((1-x)^(n)-1)/(x)

lim_(x rarr0)(1/x)^(1-cos x)

lim_(x rarr 0) (1-ax)^(1/x) =

lim_(x rarr 0^+)(x e^(1//x))/(1+e^(1//x))=

lim_(x rarr0)(cot x-(1)/(x))/(x)