If `f(x)` is a polynomial of degree `<3,` prove that `|1af(a)//(x-a)1bf(b)//(x-b)1cf(c)//(x-c)|-:|1a a^2 1bb^2 1cc^2|=(f(x))/((x-a)(x-b)(x-c))`

If f(x) is a polynomial of nth degree then int e^(x)f(x)dx= Where f^(n)(x) denotes nth order derivative of f(x)w.r.t.x

Let f(x)=(x^(3)+2)^(30) If f^(n)(x) is a polynomial of degree 20 where f^(n)(x) denotes the n^(th) derivativeof f(x) w.r.t x then then value of n is

If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degree n in tan x, then the value of n is

If f (x) is polynomial of degree two and f(0) =4 f'(0) =3,f''(0) =4,then f(-1) =

Evaluate: intf(x)/(x^3-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3

Suppose f(x) is a polynomial of degree four , having critical points at - 1,0,1. If T = (x in R|f (x) = f(0)} , then the sum of sqaure of the elements of T is .

Let f(x) is a polynomial of degree four satisfying f(15)=7 and f(6)=f(8)=f(7)=f(9)=11, then f(1)-f(2)+f(3)-f(4)+.........+f(13)f(14)+f(15) is equal to.

If f(x) is polynomial of degree 5 with leading coefficient =1,f(4)=0. If the curvey y=|f(x)| and y=f(|x|) are same,then find f(5).

Suppose f(x) is a polynomial of degree 5 and with leading coefficient 2009. Suppose further f(1)=1,f(2)=3,f(3)=5,f(4)=7,f(5)=9. What is the value of f(6)