If `lm_(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 lim_(x rarr oo)f(x) is finite and non zero and lim_(x rarr oo)(f(x)+((3f(x)+1)/(f^(2)(x)))=3 then find the value of lim_(x rarr oo)f(x)

lim_(x rarr oo) (1+f(x))^(1/f(x))

Let f:rarr R rarr(0,oo) be strictly increasing function such that lim_(x rarr oo)(f(7x))/(f(x))=1 .Then, the value of lim_(x rarr oo)[(f(5x))/(f(x))-1] is equal to

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

Let f(x) is a differentiable function everywhere and suppose lim_(x rarr oo)(f'(x)+3f(x))=12 then lim_(x rarr oo)f(x) is equal to

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is

If (lim)_(x rarr c)(f(x)-f(c))/(x-c) exists finitely,write the value of (lim)_(x rarr c)f(x)

If f(x)=(1)/(3){f(x+1)+(5)/(f(x+2))} and f(x)>0 foe all x in R, then lim_(x rarr oo)f(x) is

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim_(xto oo)f(x) is