If `f(x)=sqrt((x-sinx)/(x+cos^2x))`, then `lim (x->oo)f(x)` is

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

lim_(x->oo)sinx/x =

Evaluate lim_(xto oo)sqrt((x-sinx)/(x+cos^(2)x))

Evaluate lim_(xto oo)sqrt((x-sinx)/(x+cos^(2)x))

lim_(x->oo)[sinx/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

{:("Column-I","Column-II"),(A.f(x) = (1)/(sqrt(x -2)),p.lim_(x to 0)f(x) =1),(B. f(x) = (3x - "sin"x)/(x + "sin" x), q. lim_(x to 0)f(x) = 0),(C.f(x) = x "sin"(pi)/(x) f(0)=0,r.lim_(x to oo) f(x) = 0),(f(x) = tan^(-1) (1)/(x),s.lim_(x to 0) "does not exist"):}

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

If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")_(xrarrpi/2)f(x)=-oo (b) ("lim")_(xrarrpi/2)f(x)=oo (c) ("lim")_(xrarrpi/2)f(x)=oo (d) none of these

If f(x)=sqrt(x^2+9) , write the value of (lim)_(x->4)(f(x)-f(4))/(x-4) .