`lim_(xrarr0)(1/(e^x-1)-1/x)=?`

Evaluate the following limits: lim_(xrarr0)((e^(x)-x-1)/(x))

Evaluate the following limits: lim_(xrarr0)((e^(4x)-1)/(x))

Evalute lim_(xrarr0)((e^(3x)-1)/(x)).

Evaluate the following limits: lim_(xrarr0)((2^(x)-1)/(x))

Evaluate: (i)lim_(xrarr0)((e^(-x)-1)/(x))(ii)lim_(xrarr0)((e^(x)-e^(-x))/(x))(iii)lim_(xrarr0)((e^(x)+e^(-x)-2)/(x^(2)))

Evaluate the following limits: lim_(xrarr0)((e^(tanx)-1))/(x)

Let lim_(xrarr0)(sin2x)/(tan((x)/(k)))=L_(1) and lim_(xrarr0)(e^(2x)-1)/(x)=L_(2), and the value of L_(1) L_(2) is 8, then k is

lim_(xrarr0) ((x+1)^(5)-1)/(x)

Evaluate : lim_(xrarr0 )(e ^(sinx)-1)/(x)

The value of lim_(xrarr0)((e^(x)-x-1)(x-sinx)ln(1+x))/(x^(6)) is equal to