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 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+q| is

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

f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)), find lim_(x rarr0)f(x)

Let f(x)=lim_(n rarr oo)(log(2+x)-x^(2n)sin x)/(1+x^(2n)) then

Let for all xgt0,f(x)=lim_(nto oo)n(x^((1)/(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

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

Let f(x)=lim_(n to oo) sinx/(1+(2 sin x)^(2n)) then f is discontinuous at