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

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

If lim_(xtoa)(a^(x)-x^(a))/(x^(x)-a^(a))=-1" and "agt0," then find the value of a."

If Lim_(xrarr0)(a^(x)-x^(a))/(x^(x)-a^(a))=-1 , find 'a'

Let underset( x rarr a )("Lim") ( x^(x) - a^(x))/( x-a) = l , a gt0 & underset( x rarr a) ( "Lim") ( a^(x)- x^(a))/( x-a)= m , a gt 0 and If l = m then find the value of 'a' .

If lim_(x rarr oo){(x^(2)+1)/(x+1)-(ax+b)}=0, then find the value of a and b.

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

F(x) is the function such that (lim)_(x->0)(f(x))/x=1\ a n d\ (lim)_(x->0)(x(1+acosx))/((f(x))^3)=1 , then find the value of a

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=-

If a=lim_(x rarr0)(1-cos x)/(x^(2)),b=lim_(x rarr0)(sin3x)/(x),c=lim_(x rarr oo)(sin x)/(x) then find the value of (2a+b+c)

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