`f(x)=(a_(2n)x^(2n)+a_(2n-1)x^(2n-1)+....+a_1x+a_0)/(b_(2n)x^(2n)+b_(2n-1)x^(2n-1)+....+b_1x+b_0)` where `n in N, a_i, b_i in R and b_(2n != 0`. If domain of `f(x)` is R, then

a_(0)x^(n) + a_(1)x^(n-1) + a_(2)x^(n-2) + ……..a_(n)x^(n) is polynomial of degree ……………

Let f(x) = a_(0)x^(n) + a_(1)x^(n-1) + a_(2) x^(n-2) + …. + a_(n-1)x + a_(n) , where a_(0), a_(1), a_(2),...., a_(n) are real numbers. If f(x) is divided by (ax - b), then the remainder is

a_(0)f^(n)(x)+a_(1)f^(n-1)(x)*g(x)+a_(2)f^(n-2)g^(2)(x)+......+a_(n)g^(n)(x)>=0

lim_(x rarr oo)(a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n))/(b_(0)x^(m)+b_(1)x^(m-1)+b_(2)x^(m-2)+...+b_(m)) ; m, n>0 is equal to A. 0 when m > n B. oo when m C. (a_(0))/(b_(0)) when m=n D. none of these

Let f(x)=a_(0)+a_(1)x+a_(2)x^(2)++a_(n)x^(n)+ and (f(x))/(1-x)=b_(0)+b_(1)x+b_(2)x^(2)++b_(n)x^(n)+ then b_(n)+b_(n-1)=a_(n) b.b_(n)-b_(n-1)=a_(n)cb_(n)/b_(n-1)=a_(n) d.none of these

If (1+x+x^(2))^(n) = sum_(r=0)^(2 n) a_(r). x^(r) then a_(1)-2 a_(2)+3 a_(3)-..-2 n. a_(2n) =