" 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))

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

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

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

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)

If lim_(x rarr0)[1+x+(f(x))/(x)]^((1)/(x))=e^(3), then find the value of 1n(lim_(x rarr0)[1+(f(x))/(x)]^((1)/(x)))is=-

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-

Evaluate "lim_(x rarr0)(8^(x)-4^(x)-2^(x)+1)/(x^(2))