`lim_(x->o)(3^x-1)/(2^x-1)`

If (lim)_(x->a)(x^3-a^3)/(x-a)=(lim)_(x->1)(x^4-1)/(x-1) , find all possible value o adot

lim_(x->1)[(2x-3)(sqrtx-1)]/[2x^2+x-3]

If Lim_(x to 1) (x^(4)-1)/(x-1)=Lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , find the value of k .

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.

lim_(x->0)(2 7^x-9^x-3^x+1)/(sqrt(2)-sqrt(1+cosx))

lim_(x->2)(sqrt(x-1)-1)/(x-2)

Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)

Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)

lim_(x->1)[(x^3+2x^2+x+1)/(x^2+2x+3)]^((1-cos(x-1))/(x-1)^2)

STATEMENT-1 : lim_(x->oo)(log[x])/([x])=0 . STATEMENT-2 : lim_(x->0)(sqrt(sec^2-1))/x does not exist. STATEMENT-3: lim_(x->2)(x-1)^(1/(x-2)) = 1