If `lim_(x rarra)(a^x -x^a)/(x^x -a^a)=-1 and a gt 0` then find the value of a .

lim_(x rarr 0)(1-x-e^(x))/(x^(2)) =

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

Evaluate lim_(x rarr a) (sqrtx - sqrta)/(x -a)

If f(x)={(a+bx,x 1):} and lim_(xrarr1)f(x)=f(1) , then find the value of a and b.

Find lim_(xrarr0)(sin 4x)/(sin2x)

Evaluate lim_(x rarr 4) (4x + 3)/(x-2)

Consider the function f(x) = (x^2 - 4)/(x - 2) If lim_(x rarr a) (x^4 - a^4)/(x -a) = lim_(x rarr 0) (e^(4x) -1)/x , find all possible values of a.