If `p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1))` is a polomial in `x` , then find possible value of `ndot`

The function f(x)=(x^(2)-4)^(n)(x^(2)-x+1),n in N assumes a local mininum values of n Then find the possible values of n

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

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

If x+1/x=-2 then x^(2n+1)+1/(x)^(2n+1)=

If 1+x+x^(2)+....+x^(p)=(1+x)(1+x^(2))(1+x^(4))(1+x^(8)) then find the value of p

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is

f(x)=(x^(n)-1)/(x-1),x!=1 and f(x)=n^(2),x=1 continuous at x=1 then the value of n