The value of `Lt_(x-gt0)((1+x)^(1/ x)-e)/x=`

The value of Lt_(xrarr0)(e^x-e^-x)/x is ___

The value of underset(x to 0)"Lt" ((1+x)^(1//x)-e)/(x) is

The value of Lim_(x rarr 0)((tanx)^(1/x)+(1+sinx)^(x)) where x gt0 is equal to

Lt_(x to 0)(e^(2x)+x)^(1//x) =

Show that Lt_(x to 0)(e^(x)-1)/(x)=1

Show that Lt_(xto0)(e^(x)-1)/x=1

STATEMENT -1 : The value of tan^(-1)x+tan^(-1)(1/x)=pi/2, AA x in R -{0} . and STATEMENT -2 : The value of tan^(-1).(1/x)={:{(cot^(-1)x,x gt0),(-pi+cot^(-1)x,x lt0):}

STATEMENT -1 : The value of tan^(-1)x+tan^(-1)(1/x)=pi/2, AA x in R -{0} . and STATEMENT -2 : The value of tan^(-1).(1/x)={:{(cot^(-1)x,x gt0),(-pi+cot^(-1)x,x lt0):}