(5) Find `lim_(x->oo) (1+9/x)^x`

lim_(x->oo) xsin(2/x)

lim_(x->oo) (sinx/x) =

lim_(x->oo)sin(1/x)/(1/x)

lim_(x->oo)[sinx/x]

lim_(x->oo)sinx/x =

lim_(x->oo)2^xsin(a/2^x)

lim_(x->oo) (x-sqrt(x^2+x))

lim_(x->oo)(1-x+x.e^(1/n))^n

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then the value of lim_(x->oo) f(x) is

If f(x) = lim_(n->oo) tan^(-1) (4n^2(1-cos(x/n))) and g(x) = lim_(n->oo) n^2/2 ln cos(2x/n) then lim_(x->0) (e^(-2g(x)) -e^(f(x)))/(x^6) equals