" If "lim_(x rarr a)(a^(x)-x^(a))/(x^(x)-a^(x))=-1" and "a>0," then find the value of "a" ."

If lim_(x rarr a)(a^(x)-x^(a))/(x^(x)-a^(a))=-1 and a>0, then find the value of a.

Evaluate lim_(x rarr0)((a^(x)-b^(x))/(x))

If lim_(x rarr0)((x-1+cos x)/(x))^((1)/(x))=theta^(p) then find the value of |[p]|.

Evaluate : lim_(x rarr0)(a^(2x)-1)/(x)

lim_(x rarr0)(cot x-(1)/(x))/(x)

Evaluate "lim_(x rarr0)(x-|x|)/(x)

Evaluate lim_(x rarr 0)(sin(3x))/(x)

The value of lim_(x rarr 0) ((e^(x)-1)/x)

The value of lim_(x rarr0)(e^(x)-1)/(x) is-

If lim_(x rarr a)[f(x)+g(x)]=2 and lim_(x rarr a)[f(x)-g(x)]=1, then find the value of lim_(x rarr a)f(x)g(x)