Let `f(x)={lim_(n->oo)(a x(x-1)(cot(pix)/4)^n+(p x^2+2))/((cot(pix)/4)^n+1) ,x in (0,1) uu (1,2) and 0 ,x=1` If f(x) is differentiable for all `x in (0, 2)` then `(a^2 +p^2)` equals

Let the given function is differentiable at x = 1. f(x)={{:(lim_(nrarroo) (ax(x-1)(cot.(pix)/(4))^(n)+(px^(2)+2))/((cot,(pix)/(4))^(n)+1)",",x in(0,1)uu(1,2)),(0",",x=1):} Then the value of |a+p| is

Let f(x)=lim_(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) . then

Let f(x)=lim_(nrarroo) (tan^(-1)(tanx))/(1+(log_(x)x)^(n)),x ne(2n+1)(pi)/(2) then

Let lim_(n->oo)((x^2+2x+3+sinpix)^n-1)/((x^2+2x+3+sinpix)^n+1) . then

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1, if x is rational and 0, if x is irrational

If f(x)=lim_(m->oo) lim_(n->oo)cos^(2m) n!pix then the range of f(x) is

The value of lim_(x to 0) ((1)/(x^(2)) - cot x) equals

If f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(x)dx is equal to:

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(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