Let `f(x)=lim_(n->oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1})` ,then

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

Let f(x)=lim_(nrarroo) sum_(r=0)^(n-1)(x)/((rx+1){(r+1)x+1}) . Then

lim_(n rarr oo) sum_(r=0)^(n-1) 1/(n+r) =

Let f(x)=underset(nrarroo)(lim)sum_(r=0)^(n-1)(x)/((rx+1){(r+1)x+1}) . Then

Let f (x) = lim_ (n rarr oo) sum_ (r = 0) ^ (n-1) (x) / ((rx + 1) {(r + 1) x + 1})

lim_(n rarr oo) n.sum_(r=0)^(n-1) 1/(n^(2)+r^(2)) =

If f(x) = lim_(n->oo) sum_(r=0)^n (tan(x/2^(r+1)) + tan^3 (x/2^(r+1)))/(1- tan^2 (x/2^(r+1))) then lim_(x->0) f(x)/x is

If f(x) = lim_(n->oo) sum_(r=0)^n (tan(x/2^(r+1)) + tan^3 (x/2^(r+1)))/(1- tan^2 (x/2^(r+1))) then lim_(x->0) f(x)/x is

If quad f(x)=lim_(n rarr oo)sum_(r=0)^(n)(tan((x)/(2^(r+1)))+tan^(3)((x)/(2^(r+1))))/(1-tan^(2)((x)/(2^(r+1)))) then lim_(x rarr0)(f(x))/(x) is