`lim_(x->0)(x+ln(sqrt(x^2+1)-x))/(x^3)`

lim_(x rarr0)(x+ln(sqrt(x^(2)+1)-x))/(x^(3))

If lim_(x rarr0)(x+ln(sqrt(x^(2)+1)-x))/(x^(3))=(p)/(q) where p and q are coprimes then find the value of |p^(2)-q^(2)|

STATEMENT-1: lim_(x rarr oo)(log[x])/(sqrt(([x])/(sec^(2)-1)))=0 STATEMENT-2: lim_(x rarr0)(sqrt(sec^(2)-1))/(x) does not exist.STATEMENT-3: lim_(x rarr2)(x-1)^((1)/(x-2))=1

Let p=lim_(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

The velue of lim_(x rarr0)(sin(3sqrt(x))ln(1+3x))/((tan^(-1)sqrt(x))^(2)(e^(5(3sqrt(x)))-1)) is equal to

STATEMENT-1 : lim_(x->oo)(log[x])/([x])=0 . STATEMENT-2 : lim_(x->0)(sqrt(sec^2-1))/x does not exist. STATEMENT-3: lim_(x->2)(x-1)^(1/(x-2)) = 1

lim_(x rarr0)[(ln(1+x)^(1+x))/(x^(2))-(1)/(x)]

lim_(x rarr0)(ln(1+x)^(1+x))/(x^(2))-(1)/(x)

lim_(x rarr0)(sqrt(1+x^(2))-sqrt(1+x))/(sqrt(1+x^(3))-sqrt(1+x))

lim_(x to 0)(xe^(x)-log(1+x))/(x^(2))=