Find `lim_(x->oo) (e^-x +1/x)/(1/x^2+3/x)`

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

lim_(x->oo)(e^(11x)-7x)^(1/(3x))

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

Solve lim_(x->oo)(e^x-e^-x)/(e^x-e^-x)

lim_(x->oo)((1^(1/x) +2^(1/x) +3^(1/x) +...+n^(1/x))/n)^(nx) is equal to

Find the value of lim_(x->oo)(2-1/x+4/x^2)

If lim_(x->oo)((1+a^3)+8e^(1/ x))/(1+(1-b^3)e^(1/ x))=2, then there exists

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

lim_(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to