If `L=("lim")_(xvecoo){x-x^2(log)_e(1+1/x)},` then the value of `8L` is_____

If lim_(xtooo)x-x^(2) ln(1+1/x)=l then evaluate (25)^(l) .

If L=lim_(x rarr2)((10-x)^((1)/(3))-2)/(x-2), then the value of (1)/(4L)| is

If L=lim_(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx) , then the value of 1//(3L) is ________.

If L=lim_(x rarr0)(e^(-((x^(2))/(2)))-cos x)/(x^(3)sin x), then the value of (1)/(3L) is

Let L=lim_(x rarr oo){((x+1)/(x-1))^(x)-e^(2))}x^(2) then the value of (9L)/(2e^(2)) is equal to

If L=lim_(xrarr0)((e^(-x^(2)/2)-cosx)/(x^(2)tan^(2)x)) , then the value of 3L is equal to

If lim_(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3) , then the value of ln(lim_(xto0) [1+(f(x))/(x)]^(1//x)) is _________.

If l=lim_(xtooo)((x+1)/(x-1))^(x) , the value of {l} and [l] are

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

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