Evaluate: `("lim")_(xvec0)(2^x-1)/(sqrt(1+x)-1)`

Evaluate lim_(xto0) (2^(x)-1)/(sqrt(1+x)-1).

Evaluate: ("lim")_(xvec1)(sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrt(x)))+sqrt(sqrt(sqrt(sqrt(x-4)))))/(x-1)

lim_(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

lim_(xrarr0) (2x)/(sqrt(1+x)-1)

lim_(xto0)(sin2x)/(1-sqrt(1-x))

Evaluate : lim_(x to 0)(e^(x)-1)/sqrt(1-cosx) .

The value of the limit ("lim")_(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sqrt(x))+a^(1sqrt(x))),a >1,i s 4 (b) 2 (c) -1 (d) 0

Evaluate: ("lim")_(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I nx)))^(1/x)

Evaluate : lim_( x -> 0 ) ( 3^x - 1 )/( sqrt( 1 +x) - 1 )