`lim_(x ->a)((a^x-a^a)/(x-a)), a gt0`

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.

lim_(x rarr 0)(x^(n) ln x), n gt 0

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' .

The value of lim_(xrarroo) (logx)/(x^n), n gt 0 , is

The value of lim_(xrarroo) (logx)/(x^n), n gt 0 , is

lim_(xrarr0^(+))(x^(n)lnx), n gt0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

(i) lim_(x to 0) (a^(x) - 1)/(log_(a)(1 + x)), a gt 0 (ii) lim__(x to 0) (In (X + a)- In a)/(e^(2x) - 1) (ii) lim_(x to (pi)/(4)) (In(tanx))/(1 - cotx)