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+q| is

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then

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

lim_(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

Let f(x+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?

lim_(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equal to

lim_(xto0) (xcot(4x))/(sin^2x cot^2(2x)) is equal to

If f(x) is twice differentiable and f^('')(0) = 3 , then lim_(x rarr 0) (2f(x)-3f(2x)+f(4x))/x^(2) is

Let f(x)=("lim")_(mvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1,if x isrational 0,if x is irrational

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2