2.Evaluate `lim_(x->o)(a^x-1)/(b^x-1)`

Evaluate, lim_(x to 1) (x^(4)-1)/(x-1)=lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , then find the value of k.

Evaluate: ("lim")_(x->oo)[x(a^(1/x)-1)], a >1

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

Evaluate lim_(xtooo) x^((1)/(x)).

Evaluate : lim_(x to -1) x/([x])

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

Evaluate: lim_(x->0) (1-cos2x)/(x^2)

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

Evaluate: lim_(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

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