Find `lim_(x->oo) x`

Let f be continuous function on [0,oo) such that lim _(x to oo) (f(x)+ int _(o)^(x) f (t ) (dt)) exists. Find lim _(x to oo) f (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

If alpha in(0,1) and f:R->R and lim_(x->oo)f(x)=0,lim_(x->oo)(f(x)-f(alphax))/x=0, then lim_(x->oo)f(x)/x=lambda where 2lambda+7 is

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

lim_(x->oo)sinx/x =

Evaluate: lim_(x->oo) (x+7sinx)/(-2x+13) using sandwich theorem.

Evaluate the following limit: (lim)_(x->oo)((x^2+2x+3)/(2x^2+x+5))^((3x-2)/(3x+2))\

Evaluate the following limit: lim_(x->oo) (sin(a+x) + sin(a-x) - 2 sin a)/(x sinx))

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

Evaluate the following limit: (lim)_(x->oo)(5x^3-6) / root (9+4x^6 )\