Let `f(x)=(x+1)(x+2)(x+2^2)+..+(x+2^(n-1))` and `g(x)=lim_(n->oo)(f(x+1/n)/f(x))^n if f(x)!=0` `=0 if f(x)=0` then g(0) =

Consider f(x) = lim_(x-oo)(x^n-sinx^n)/(x^n+sinx^n) for x>0,x!=1,f(1)=0 then

Let f(x)=cos((x)/(2))*cos((x)/(4))*...*cos((x)/(2^(n))). If lim_(n rarr oo)f(x)=g(x) and lim_(x rarr0)g(x)=k then value of lim_(y rarr k)[(1-y^(2011))/(1-y)]

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

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Let F(x) = f(x) +g(x) , G(x) = f(x) - g( x) and H(x) =(f( x))/( g(x)) where f(x) = 1- 2 sin ^(2) x and g(x) =cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following If the solution of F(x) -G (x) =0 are x_1,x_2, x_3 --------- x_n Where x in [0,5 pi] then

Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ^(2). Let n be the numbers of real roots of g(x) =0, then:

Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim_( n to oo) (f(x)+x^(2n)g(x))/(1+x^(2n)) If F(x) is continuous at x=-1, then