`lim_(xrarr0)(((2x+1)^2-1)/(x))=?`

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

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

lim_(xrarr0) (x^(2)-x)/(sinx)

Evaluate lim_(xrarr0)((1+x)^(n)-1)/(x)

Evaluate lim_(xrarr0)((3^(2x)-1)/(2^(3x)-1)).

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)))

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

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

Evalvate lim_(xrarr0)((1+x)^(4)-1)/(x).

lim_(xrarr0)(cos (sinx)-1)/(x^2)=