(d) Find `lim_(x->oo) x^me^-x`

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

lim_(x->oo)sinx/x =

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

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

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

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

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

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

Let f(x)=x+sqrt(x^2+2x) and g(x)=sqrt(x^2+2x-x) , then which of the following is/are true. a. lim_(x->oo)g(x)=1 b. lim_(x->oo)f(x)=1 c. lim_(x->oo)f(x)=-1 d. lim_(x->oo)g(x)=-1

Let f(x)=(log_e(x^2+e^x))/(log_e(x^4+e^2x)) . If lim_(xrarr oo) f(x)=l and lim_(xrarr-oo)f(x)=m , then